Hi - as I understand it, to measure a single star or even to perform astrometry on that star, you can track it perfectly OK with alt-az. You need a wedge for ccd astrophotography to prevent the outer stars being seen to rotate over a long exposure, but for a variable star you will have that as your only object of interest in the centre of your view.

At least I hope that's true because it's how I'm planning to work ;-)