Well, not to flame you or anything, but you are considering doing something that is very dangerous so humor is necessary. You may need to be careful with your work though. If you are on limited duty because of the injury and they find out that you went diving with said injury, you could have problems with work. Or you could have problems with your insurance company should it find out that you went diving after the surgery. Your doctor is going to limit your lifting capabilities after the surgery for a long time and since dive gear is heavier than your lift limitations will certainly be (no lifting under 10 lbs etc), you are going to have some problems.
Since the humor is not what you are looking for, maybe some realistic advice will help. Seriously, dont do it. It could get really bad and you could put you and your buddy in serious risk of getting hurt a lot worse than where you are now. Hopefully you and your buddy have thought this through and since you have a buddy who is great and will help out when needed and is still willing to dive with you given this injury, I suppose you could do it. Is your buddy rescue certified? I still would not, even if Jacques Cousteau and He-Man were my buddies (if Jacques was living still and He-Man were real).
Should you still be medicated, you should not dive. Just like drinking or other drugs before diving. No need to say anything further
If you are going to do this, you might want to try doing this in a pool first. It would be safer than doing it in open water somewhere.
As for gear configurations: You should be able to use your inflator hose with your right hand in its normal position. Depending on your bc that is. On mine I would not be able to as I have an i3 so the inflator is on my left hip. Just cross your right arm over your chest, grab the hose and off you go. If you try to move it or drape it across the back of your neck, it would be to short to have on your right side. You should have a dump valve on the right side to getting rid of the air should be ok if you could not deflate the bc with the hose.
As for exposure suit, so long as you can get your arm in the suit with out the pain, I guess it is doable. Again, I would not do it since you would be potentially re-injuring yourself or delaying the healing process. Dive gear is not as flexible as cotton T-shirts or other street clothing so it is obviously harder to get into. Getting gloves and boots on would not be easy also. I think the gloves would be worse though since you use your bicep/tricep/forearm muscles to it get it on as well as your shoulder.
Once you got your arm in your suit, you could get your bc on but unlatch your left shoulder strap before you slip it on. Then reconnect the two strap pieces together under your arm. It may cause some pain but since you are in a fix to get wet, it might be ok. The weight of the BC might be to much on your shoulder though. You could get your gear on in the water to help reduce the weight on your shoulder.
As for putting on fins, if your buddy is holding the extra one and mask while you strap yourself in with the spring straps it should be ok also.
Since you probably dont NEED your left arm during the dive, I guess you will be ok. However, the extra steps, help needed, and serious possibility of re-injury would keep me out of the water until I was told it was ok by the doctor. If it were me, I would get in a therapeutic pool or hot tub with my snorkel before I tried to do what you are thinking about doing. But that is just me. Good luck to you. Hopefully you will get healed fast and be able to get in the water safely, responsibly, and comfortably soon.
I know I would not dive with that injury nor would I dive with you if you had that injury. As a buddy you would be practically useless, I would think. How would you be able to task manage during the dive? Inflate your BC, put your fins on and all the other stuff to dive. Even just gearing up takes two hands for me. 
