Viht's online 357 data now specify SPMs for the 357 Magnum, but its last printed reloading manual (No.2 published 1995) specified Winchester
WSR primers. I queried that at the time wondering if it was a misprint, but was informed that no, that was correct. Comparing N110 charges for the 158gn Speer JHP which is the bullet listed then and now, charges have
risen over the 30 years. In the 1995 manual start was 13.7gn / max: 15.1gn for 33,300 psi. Today, it's 15.1gn start; max: 15.9gn, pressure no longer provided. {Edit: looking at the general introduction blurb to the cartridge in the 1995 publication, it says
Primer: Small Pistol or Small Rifle', but actually uses the WSR rifle primer in the loads tables.]
SR primers will fit pistol case primer pockets but have a thicker cup according to research that James Calhoun published on this years ago, the thinner rifle models at 20 thou' vs 17 for the pistol type. They may be harder too so the combination might produce unreliable ignition with hangfires and misfires from light strikes with revolver firing mechanisms. Chemically, SPMs aren't necessarily the same as standard SRs either as they may use different mixes in the explosive pellet to suit the likely powders and charge weights in their respective cartridge types. So, if you want to try SR primers use the thinner cup / structurally weaker models (CCI-400; Remington 6 1/2; Winchester WSR; standard Russian SR which are the old PMC copper colour Small Rifle or the more recent Murom 'Competition' Small Rifle, both works code KVB-223). Magnum and match SR models use thicker/harder cups and therefore best avoided.
I suspect you wouldn't have any problems especially with N110, but as always drop charges and work up again, and desist immediately if you suffer a hang or misfire. Here's what Sierra says on the Issue:
Primer Substitutions - Sierra Bullets.
which doesn't help you much as it says you're out on a limb very much on your own unless you can find listed pressure barrel data for such a switch, which I'm pretty certain you won't.