Check out https://wow.gamepedia.com/API_SetBinding
Just have it click your button.
However I strongly recommend that you add some code to prevent your script from executing during combat using InCombatLockdown(). Otherwise your code may fail in usage at random, at least to other users than yourself and other developers. Hopefully the WeakAura author will provide some helper functions soon since I see more and more WA scripts that create secure actions without ensuring they're in a state to do so (non trivial to schedule it after combat in an efficient manner for individual scripts).