What Kind of Outlet Allows 1 In-Wall Light Switch w 2 Outlets to Control 2 Sconces w Semi-Independent On/Off Buttons & Outlets on Each?
Your switch sounds like a normal single pole switch.  Someone basically wired up the switch to the sconce which already had switches so they could leave the sconce switch on all the time and turn both sconces on with the wall switch only.

So nothing fancy - you should be able to just get a standard outlet to replace the wall switch and run the line to the sconces as "load" from the new outlet.  However since this is a bathroom you might want a GFCI outlet as extra protection.