Don't do "diamond pushups" or "close handed pushups" then. Just line your body up, hands beneath shoulder joints. Bringing your hands in closer together really is not going to give you anything new or different than you cannot get doing regular pushups -- you'll just FEEL it a little differently, but a pushup is a pushup, and the same muscles are recruited.
It is not worth it to feel it a little differently, for the price you pay of torquing your joints in unnatural positions while bearing weight. Shoulders and wrists are pretty complex joints. They will be in the strongest position if you can try to maintain a natural body alignment. Having your hands too far out or in will give you a different sensation but your joints were not designed to function bearing weight at those sharp angles.
I'm not sure what you're tyring to accomplish with this exercise, but I'm sure there are other exercises you can do to target similar muscle groups without being so harsh on your joints.