Will S&W sell you the parts to convert to a thumb safety on an m&p9 compact?

If not, how do I get them?

Not sure about the 9c but I installed one on my M2.0 compact and it was fairly simple. I ordered the parts from Midwest Gunworks. There were 3 parts (safety lever, detent, detent spring) that ran $35 combined. The frame already had a cutout so it wasn't difficult. I seem to remember there were YT videos showing how to do it.

S&W won't sell you the parts. Depending upon what model & production run of the frame, it may/may not need cut for the safety. IIRC, the sear block was somewhat different on the 1.0.

I got my OE parts from Ebay. I think Numrich has them too. Dead easy. Someone will want to buy your plugs, or if you know someone who wants to delete their safety, you can just swap