What ammo you use and how often you use it, will determine how long your model 37 will function.
The alloy guns, like the S&W model 37 were basically clones of the steel framed guns ( like the S&W model 36) and not designed from the bottom up as a new design They will function for a long time if you use only standard pressure, standard velocity ammo. That was what the original steel framed guns were designed for. Aluminum is not as strong as steel, but the original steel used by the gun designers in the 1950's was probably not as strong as that available now.
You may have heard of the problems with using +P ammo, in the past. One of the reasons that law enforcement agencies dumped the .38 Special in large numbers were the problems they had with the steel framed S&W K-frame revolvers when using +P ammo. The guns when fired a lot, as they are in law enforcement organizations, tended to go out of time and suffer from frame stretching. Most older aluminum framed revolvers are not recommended for the use of +P ammo by their makers.
The question is can you practice with what you carry?
Using only .38 wad-cutters at the range and carrying +P ammo on the street will not give you a good training regime.
I use standard pressure loads for training. I like the old 130 grain fmj Air Force load, which is made by all the major makers or the 158 grain lrn police load, also made by everyone. They are usually cheaper than .38 wad-cutter ammo.
For carry, I use the WINCHESTER 130 grain Train & Defend jhp load. Recoil is similar to the 130 grain Air Force load. The problem is finding them.
I have also used the HORNADY 110 grain FTX - Critical Defense loads. They work well and seem to be more commonly available, but the point of impact is farther from the point of aim.
Be careful with some of the "boutique brand" ammo. They get higher performance out of the .38 Special and other calibers while claiming to be standard pressure, but even if standard pressure, a higher velocity round will have more recoil that will be harder on the shooter and the gun frame.
Good luck,
Jim