You could do it, but it’s going to be complicated.
The hue bulbs connected directly to an echo show/plus are not going to show up in your smartthings app, so you will have to use an Alexa routine (not a SmartThings routine) as an intermediary.
I’m going to list the steps below, but bear with me, because I know this is complicated. it would indeed, as you guessed, be way easier if you were using a Hue bridge. (at which point your hue bulbs would also show up as individual devices in your smartthings app). But you don’t have to have that device to make this work.
OK, here goes.
- Create a virtual device in SmartThings. If you have a smartthings hub, you can do this with an edge driver, which future proofs it because that works with the new architecture
If you don’t have a smartthings hub, as of the time of this writing, you can still create a virtual device using just the IDE (the web interface to your smartthings account), but that device will be using the old architecture and I don’t know what’s going to happen once that goes away, probably in a few months. But you could do it for now.
Here’s the community FAQ on this step:
FAQ: Can I trigger an Echo Action without Speaking to It?
So at the end of the step, you have a virtual device which will show up in your smartthings app and which will also be usable in an Alexa routine.
If you used a “momentary“ switch for your virtual device, then it will automatically turn itself off again each time, so it will be available to use again the next time.
In your case, you might prefer a virtual device which turns on and stays on, so you can have turning it off trigger a different scene, but that just depends on the details of what you’re trying to do.
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now you have to create a scene in the smartthings app to turn your virtual device on. At the time of this writing, the smart tags could be set up to trigger a smartthings scene, but they cannot be used in other smartthings routines/automations. So we just want to have a button press on the galaxy tag activate the SmartThings scene. Remember that since the individual hue lights connected directly to the echo show won’t show up in the smartthings app, all we need the scene to do is to turn on our virtual device.
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now create an Alexa routine (not a smartthings routine) using the Alexa app so that when that virtual device turns on, whatever you want to have happen with your hue bulbs will happen.
https://www.amazon.com/gp/help/customer/display.html?nodeId=202200080
You will probably need one Alexa routine to turn the bulbs on and a different one to turn the bulbs off, but again it depends on the details. 
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So…. You can do it with your existing equipment. But the setup is pretty complicated.
BTW, this is the same method you would use to have a galaxy tag control any device that Alexa can see in its routines but smartthings cannot see in its app.
Tagging @SamsungZell