My understanding is that the breech face for the 9mm is a little smaller than the .40.... However, it should work anyway.
I don't think you can go the other way, though....
The Storm Lake barrels come well recommended, and I think will fit better than an S&W "parts" barrel.
I put a 9C slide & barrel on top of a 40C frame (and vice versa) with no issues at all. The 9C turned up with a thumb safety that I preferred on the 40C.
AFAIK, the recoil springs are the same. You will need 9mm magazines, too....