Your 357 Sig cases will be the proper size, but there's the possibility that the case mouths may have been battered in transit, and with this round you'll find it necessary to slightly bell the case mouth anyway. I also chamfer the insides of the case mouth for this round, since it needs tight tension to hold the bullet in the short neck, and I don't bell it much at all.
Take the sizing die out of your press and load as normal. The over all length on this cartridge is critical, as well as the neck tension I mentioned. This is a high pressure round, higher than .40 S&W, so you don't want bullet setback with it, which would increase pressure. I've found that powders that are slightly compressed help to prevent bullet setback. My favorite powder for 357 Sig is Accurate #9, which gives exceedingly excellent accuracy in both of my handguns chambered for it.
Hope this helps.
Fred