Dips are a better move to perform.
If you're shoulders do not like dips, then I would cut your benching down, and work the shoulders to improve their strength, and flexability to allow dips.
This aspect of making sure you're shoulders are in good shape, and developed properly is something I have often talked about. Ler's not forget that banching is a compound move. A large part of a proper bench movement involves the front delt.
A lot of people are front delt heavy, and imbalanced in their delt work. Make sure you have good balance in your shoulder program.
This talks a bit about some aspects of pressing that are often overlooked
T NATION | Are You Ready to Overhead Press?
Upper back, delts, and chest all need to thought of together when thinking of upper body work.