Only you know, saxophoniac3 — there are some pretty good clarinet players who use a strap but you can find a lot of criticism of the practice as well. What I've found, as doubler (whose tennis elbow forced him to sell his Mark VI soprano a few years ago) is that a neckstrap doesn't support the clarinet at the right angle. It tends to pull the instrument toward the body and the subtle force used to put it in the proper position ends up hurting more than just supporting the weight of the clarinet without the strap. But my problem is with the elbow, not the wrist. You might not be holding the instrument properly or it's possible an after-market improved thumb rest would help. You might also be helped by doing some dedicated strength exercises with a small barbell. But basically, if it works for you — and you can avoid developing "bad habits" — you're probably better off not punishing your body.