What’s the brand and model of the current wall switch?
And in particular, is the remote an IR remote or is it a radio frequency remote? One of the easiest ways to tell quickly is if the remote works from outside the room with the door closed, so that the signal is going through the wall, it’s probably an RF remote. IR remotes need to be line of sight.
If it’s an IR remote, there’s a good chance that it would work with the Logitech Harmony hub. And if it works with the Logitech Harmony hub, you can get integration with SmartThings that way without having to do any rewiring at all. But you would have to buy a Logitech Harmony hub for that room if you don’t already have one. You would also be able to use the Harmony for other purposes at the same time, such as controlling a television. But for this to work it has to be in the same room with the fan switch.
If it’s an RF remote, then you’re out of luck and you probably have to replace the switch and start from the beginning.
But I did just want to mention the harmony option in case it was something that might work for you.
Here’s the site where you can look up what fan remotes are compatible with harmony:
https://support.myharmony.com/en-us/compatibility
The following is the harmony hub that is compatible with smartthings. Price varies a lot, I often see the least expensive price at Best Buy, but sometimes Amazon has it at a good price so it’s worth checking around. To make the fan switch option work, all you need is the harmony hub itself. But you can also buy it in a bundle with a button remote.
http://www.bestbuy.com/site/logitech-harmony-home-hub-black/1483019.p?skuId=1483019
Again, this won’t work with all set ups, but it is worth checking to see if it might work with yours. 