I wouldn't skip the bench, it's important to develop that movement. I agree with the poster who said to use a narrower grip. This will de-emphasize your pecs and put more stress on your arms. It's also healthier for your shoulders to bench with a narrower grip so it's a win win for you.
The next time I stall on the bench press and have to reset my program at a lower weight, I'm going to move my grip in a little narrower just for the long term benefits to my shoulders.