.38 will do the job if you get it where it needs to go. I personally just dont like shooting them out of .357's, and prefer to keep things caliber specific.
If youre sloppy on your hygiene, and allow those .38 "rings" to build up in the in the .357 cylinders, youre going to have issues, if and when you want to stuff .357's in there.
Another issue I seem to always have too, for some reason, when I shoot hard cast .38 LSWC's, or lead bullets in general out of my .357's, they seem to want to lead the barrel, forcing cone, chambers and face of the cylinders in my guns, and my lead .38's are not loaded hot. Trying to de-lead the guns all the time, gets old in a hurry.
What kind of snubby is it? The J frames (especially the Airweights, but even the steel versions), etc, can be a chore and a challenge to shoot, even in .38. Its kind of a Catch 22 type thing sometimes. You need to practice with loads close to what you intend to carry to get and stay good, but because of the critter youre shooting, practice is usually painful, sometimes to the point of being brutal, and you end up dreading practice, and dont.