It's hard to predict if they will crack the barrel. I've read posts by some who have claimed that they had cracked the forcing cone with less that one full box of the Super Vel ammo back in the 70's. Now, on a positive note, I strongly doubt that your WWB is loaded anywhere near the power levels of that old Super Vel. One thing to try is looking for the ballistic data for that WWB, if the muzzle energy is 500 ft.lbs. or less it's likely to be harmless. Same thing in regards to that Remington JSP.

However, if you want to be 100% safe, regard that particular lot of ammo in your posession as a reason to purchase a 686 or 627. Come on, admit it, you really do need another 357 Magnum, one just isn't enough.

As for your question regarding +P ammo, that won't be a problem, by SAAMI specs. almost any 38 +P you can find will generate only about 250 ft.lbs. of muzzle energy and that's not even close to the 700 ft.lbs. that a hot 357 Magnum commercial loading can generate.

BTW, I've excluded both Double Tap and Buffalo Bore ammunition from being considered "commercial", both these makers produce ammunitions that are at SAAMI maximums or perhaps just a bit over SAAMI maximums. Basically, they are great hunting ammunitions but a lot more powerful that I would care to use for casual shooting in something as light as a K frame.