Skip the wrist wraps.
Start at lower weights that your wrists can handle. As you build up your arm strength, you won't need wrist wraps.
It might be an ego crush to go back down in weight on the bench press, just deal with it. Supplement your chest workouts with either dumbbell flyes or pec deck exercises.
I've also been doing reverse wrist curls (light E-Z bars) and reverse bicep curls as well. It's helped tremendously.