Buy a SmartThings hub ($69)
Set up a virtual switch in SmartThings IDE.
Stringify can now control that virtual switch.
Connect SmartThings to Alexa
Set up Alexa routines to turn the Alexa switch on/off with the SmartThings virtual switch.
...but once you've done that, might as well just return the Alexa switch and buy a switch that is directly compatible with SmartThings. (Switches connected to SmartThings are ALSO compatible with Alexa, by the way, so it's not one or the other).