The simplest solution is probably to use the Lutron Caseta switches. These are very well engineered and the company has a number of patents on switch design so they generally can work with more retrofit situations than other brands.
Their usual approach is to use a wired switch for the master and then one of their pico battery operated switches at each auxiliary position. The pico battery is good for 10 years and these are very reliable and quick. You can also do dimming from the auxiliary position.
There is an official SmartThings integration which will require that you also get the Lutron SmartBridge. One smartbridge can support up to 40 Lutron devices. You can get a starter kit which has the SmartBridge, a master dimmer switch, and a pico, and in that case the smart bridge is only about an extra $20.
https://www.amazon.com/LUTRON-P-BDG-PKG1W-Wireless-Lighting-Starter/dp/B00MXCRAX8
If you just want white switches, these are widely available including at Best Buy, Home Depot, Lowes, Amazon, etc.
If you want black or almond or other colors you will have to get them from one of the specialty retailers like Westside wholesale.
https://www.westsidewholesale.com/lutron-pd-6wcl-bl.html
The Caseta line also has its own native integration with echo, Google home, HomeKit, and harmony just in case that’s of any interest. It does give you a Plan B for voice control if SmartThings is ever unavailable.
One more thing to know: If you get the bridge from the starter kit, then the Picos will always be invisible to SmartThings. They will just work to operate their associated master switch. If you want to use those for other things with SmartThings, you will have to get the smart bridge pro and do some other technical stuff. Most people don’t do that, but I did want to mention it up front because it does change which bridge you should buy.
You can get more information about the Lutron integration in the following thread:
If you want to go back to considering the GE switches, talk to the people in the following thread. They may have some additional wiring suggestions: