Terry: I don't have the 637 but I have an Airweight Bodyguard, the Model 38 with the aluminum frame, and I love it. I've had it for a number of years and carry it regularly. Mine is not +P rated but I shoot 200 grain factory reproduction loads exclusively, unless I just want to blow off some old reloads, and she doesn't hic-cough a bit. I used to use the CP 200 gn swc but recently purchased the same from Mt. Baldy.
That 637 should serve you well. If, at some time in the future you start not to like the recoil or blast from the +P loads, you can always go to that 200 grain load - it shoots at a lower pressure than the +Ps - actually, the same pressure as the wadcutter loads. HTH. Mikey.