I read somewhere that wadcutters tend to tumble when the get into a body. Wheter or not it's true I don't know!
That said I think you should know that Federal is reintroducing the old "Chiefs Special" load the S&W pioneered a long while back! What it is, is a dead soft 125gr HP coated in nylon (hence the name "Nyclad") that does expand out of snubbies and was designed with airweights like your model 37 in mind.
I have used this load in my model 60 and 49 before realizing they'd take a little +P without turning to dust. But if I owned a 37 or any other airweight, I load it with these Nyclads!
For use on critters, either will do the job. Dale

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"Long live the S&W 3rd. Gen.!"