Not that I would EVER tell anyone to do as I did, but I carried a Smith Mod. 37 for years while still on "The Job". I must have fired over 500 rounds of +P ammo through that aluminum framed gun, and it was not even rated for +P. As a matter of fact, Smith said "Don't use +P in this gun."
OK, that being said, I never had any problems with the piece shooting loose, and depended upon it to protect my life for a good number of years. When I retired, I gave the 37 to my son, and he still carries it on a daily basis. With +P ammo.
When I realized how stupid I was to give the 37 away, I got a 642, which IS rated for +P ammo, and have never fired anything else through it. So far, about 2500 rounds. I don't think you have anything to worry about.
Shoot it till you are too old to enjoy it, and then give it to your grandchild.