Yes, unfortunately, that switch will not work for you.
There is one very good option that does not require a neutral wire and now has an official integration with Smartthings: the Lutron Caseta line. Most of their models do not require a neutral wire. You will however, have to get a Lutron SmartBridge (one SmartBridge can support about 40 individual switches) in order to make the integration work. But these are very well engineered switches, easy to install, and very quick. I use them in my own house.
There are a couple of other options you can look at, but the Lutron will be the simplest.
(Lutron is an engineering company focused on lighting and holds a number of patents on their devices, which is why they can do what nobody else can for several features.)