You'll be fine, and so will your arrow flight. Mechanical releases were around long before centershot risers and plunger rests. Paradox is more a function of dynamic arrow spine than anything else. An arrow shot from a drop-away rest with a release still needs to be set up correctly to recover from paradox.
I can't make a recommendation on type of release beyond go to an archery shop and try a bunch out to see what is most comfortable. Also make sure it's adjusted correctly for you! I can't tell you how many Bowhunter Ed students I have come through the class where their release length is really screwed up!
It'll limit your shots somewhat - no quick shots at rabbits, treerats or pheasants, but you need to do what you need to do to keep shooting!