S&W's answer would be no. Back when I had an old 37 like yours I used some pretty hot loads in it and never noticed a problem. Those were hand loads and not OTC +P which has a pressure rating only barely higher than standard loads. I don't recall the exact numbers rat off the top of my head but I think they are around 18,000 and 21,000 psi or cup depending on who's data.
I'm not telling ya it's OK just passing on what I did when I had one. I believe the newer ones but not sure the start date on it are all +P rated.