If we ignore smartthings for the moment, The only option I can think of given the constraints you have, would be to use a non internet based controller, a battery operated switch, and a smart light bulb on the same protocol. The lightbulb will appear as a dimmer switch to the controller. You would have very few rules options, but you probably could set time based schedules. You could definitely have the smart bulb controlled by the switch.
I can think of two different set ups that would work with these Constraints, but you would have to match these models exactly.
This is older technology, and you would have to use the specific models. You do the programming on a tabletop console or the battery switch itself which does not require a smartphone or Internet. After that, the bulb would appear to be a dimmer switch and the Battery switch Would work with it. the bulb would have to be within around 40 feet of the switch, but the signal will travel through walls.
Option 1: pre smartphone Z wave setup plus zwave smart bulb
Back before smartphones, both Eaton Cooper and Leviton Offered simple tabletop controllers which could establish a Z wave network. You could use either of these. They tend to run around $150 each, sometimes a little less. I don’t remember how many devices these controllers can handle, you would have to check the specs. It might be as low as 16, but if I recall correctly it’s 32. But check. There’s a hard zwave maximum at 231 per network, but I don’t think any of the tabletop controllers can handle that many except the Eaton Cooper which was the newest of the old technology controllers.
https://www.amazon.com/Cooper-Wiring-Devices-RFTDCSG-Controller/dp/B004FVXPQQ
Then you have a choice of a couple of battery operated zwave wall switches. Eaton Cooper makes a nice looking one, Called the anyplace switch. It will function as a dimmer. It’s available in two styles and several colors. It exactly matches the style and color of their mains-powered switches if that’s of any interest as well.
https://www.amazon.com/Eaton-RF9500AW-Aspire-Battery-Operated/dp/B004I7YSVI/
Ecolink has an Uglier but cheaper one which is a physical relay and makes a loud click. That one does not dim.
And gocontrol makes one with two buttons, on or off. This will cost between 30 and $80 depending on whether you can get it on sale. This model can also be used without the table top controller, but you will get fewer rules options with it. On its own it can control up to ten zwave bulbs.
https://www.amazon.com/GoControl-WA00Z-1-Z-Wave-Scene-Controller-Switch/dp/B01BKWG9XS/
Then you need a Z wave (not zigbee) lightbulb. GoControl makes these. Typical cost is around $18 per bulb, but shop around, prices vary a lot on these. (Don’t bother with the color-changing bulbs: this setup can’t change color anyway. Just on/off/dim.)
https://www.amazon.com/GoControl-Z-Wave-Dimmable-Light-LB60Z-1/dp/B00PJH16UC/
Note that some of the tabletop controllers can also work with other device classes also such as motion sensors or contact sensors so it’s a real Z wave network, not just for lighting, but with very limited rules programming.
You can mix and match the devices I’ve listed under this option, so you could use a Leviton tabletop controller with an ecolink switch, etc.
There’s also a GE option for the controller, but to be honest I’m too tired to look it up right now. Those definitely have a limit on the total number of devices each controller can handle, and there are some other issues with them. They’re OK devices, I just personally don’t like them very much.
Eaton Cooper makes the nicest brochures for their line if that matters to you. (Eaton is the company, Cooper is the division, and Aspire RF is the model line for the smart devices. You’ll find the products listed under any of these 3 names.)
http://www.cooperindustries.com/content/dam/public/wiringdevices/products/documents/brochures/aspire-rf-brochure.pdf
Option 2: zigbee operated dimmer switch plus zigbee smart bulbs
This is a brand new option just made available in the last year or so. They are currently available from two different brands. In this case the switch itself acts as the controller and can typically handle up to 10 lightbulbs (grouped) per switch.
These switches don’t look like a conventional switch, For one thing they are quite bulky, but they fit in a one gang space and surface-mount on the wall. These are intended specifically to control the smart bulbs, you can’t add anything else to them like sensors. And you can’t program them beyond on /off/dim for the bulbs. Typically one switch can control up to 10 bulbs as a group and the range is around 30 feet from the switch (again the signal can go through the wall).
Phillips hue has a dimmer kit which consists of one battery-operated switch and one dimmable white bulb and then you can add more bulbs to it. This usually sells for under $35 and additional individual white bulbs sell for around $15. Home Depot should carry these. Nice packaging, widely available, super easy to deploy and use. Only comes in one color and the one style.
Note that you do not use the “Phillips hue bridge” in this configuration—That one requires a smartphone to set up while if you just use the dimmer Kit you don’t need a smartphone.
https://www.amazon.com/Philips-Dimming-Installation-Free-Exclusive-Assistant/dp/B016AEHU70/
Sylvania Smart+ ***(Formerly called Sylvania lightify)***. You buy everything separately, in this case one dimmer switch and then individual bulbs. I think that limit is also 10 bulbs per switch but check the specs. The biggest advantage to this is that the bulbs come in more shapes and sizes. But their marketing materials make the switch look smaller in the pictures then it actually is, which annoys me. 
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https://www.amazon.com/SYLVANIA-LIGHTIFY-Adjustable-SmartThings-Assistant/dp/B01G8ILYRA/
Note that although this may say they work with Amazon Alexa, they won’t unless you also have Internet connection and a hub/Gateway. In the configuration we are talking about, just one switch and some bulbs, you don’t get any voice control.
So that gives you a couple of options. The zigbee choice will be cheaper but can only work with lightbulbs. It will also have a slightly shorter range than zwave, but since these are the older Z wave models, it’s the difference between about 30 feet and about 40 feet.
Again, you won’t need a smart phone, internet, WiFi, or the SmartThings hub for either of these options, but they are basically just going to give you a battery operated switch to control a smart bulb.
And remember that in these configurations, the bulb and the switch must match protocol: You can’t use a zwave bulb with a Zigbee switch or vice versa. If you want to do that, you have to go to one of the multi-protocol hubs like smartthings, and that in turn would mean Wi-Fi, Internet, and a smart phone.
You could hold the switch in your hand, and it would work just as well. It’s just sending a wireless signal directly to the bulb, it doesn’t care how the fixture is powered as long as it is powered on. It’s the bulb which decide how much power to draw from the fixture, so when it looks like it’s off, it’s actually still drawing a small amount of power for the internal radio. That’s how it can hear the next “on” command from the radio in the switch.
