Jack,
I don't know about the M&P 22 Compact but suspect it's the same general mechanism as the other M&P models. I have an M&P45 full size frame that I bought used with the large batwing ambi safety in place. I do not like or want a manual safety on my guns. I tolerate one or two that have them, but they are single sided and very small and unobtrusive as well as very positive in operation so I've left them along. I've never had one to move from it's "off" position. On the 45, the safety moved back and forth easily and I detested it. After some discussion with other owners, I removed the rear pin in the frame and raised that part of the inner mechanism up in the frame just high enough to allow me to remove the safety lever mechanism by itself. The ambi safety lever is a one piece affair consisting of the two batwing outer portions attached to the "bar" that crosses the frame and operates the internal safety mechanisms. It just lifted out and I returned the inner mechanism block back to it's original position and replaced the pin. It has worked perfectly with out that piece in place and never have had any problem with it since removal of the piece. There are two "slots", one on either side where the bar extends outside the frame to the external safety wings. They make small plastic plugs that are supposed to fit those slots to fill them. They are small and do not bother me to leave them unplugged. They can be seen but you kind of have to look for them, so I did not elect to plug them.
As I said, I'm just speculating, but you should be able to take a look at your frame with the slide off and see the piece that needs to be removed if it's the same as the larger framed M&P's. I have also heard of a couple of owners who removed the piece, sawed off the left hand side at the point where the bar extends through the frame and then replaced it to retain the safety on the left hand side of the frame for right hand operation. This might be an option for you. Again, no experience here with your handgun, but I see no reason why that portion of the external safety lever on the right side of the frame cannot be removed because the remainder of the safety will still be captured as it was and is.
I just report this for your information in case it might be helpful to you. Hopefully someone with actual experience with the .22 Compact model will be able to provide better answers to your question. Good luck!