For a standard pressure load, I'd be inclined to try out Winchester's 130gr Defend JHP load. It seems to perform reasonably well in gel, though I'm unaware of any actual shootings with it. My actual favorite is Federal's 125gr Nyclad, but it's been discontinued for a while now and I'm hoarding the last couple of boxes I have.
I prefer HP to solid bullets because I think the HP will be more likely to damage tissue even if it doesn't expand due to a "cookie cutter" effect, if you will. How much of an advantage that might be, I can't say, but the only things we can control is bullet choice and shot placement, with shot placement being the more important of the two. If I can get a slight edge in terminal performance, presuming it doesn't negatively affect reliability or shootability, I'll take advantage of that.
To your specific question, if I had to choose between SWC or WC, I'd probably go with the WC because I think the flat meplate may have an advantage when it comes to tissue disruption over the SWC (again, I can't say for sure how much of an advantage that would be, and hard cast would be better than soft cast in that regard) and in gel tests they will actually penetrate within the FBI range of 12-18" when fired from a 2" barrel. I can't say for sure, but I think the SWC may exceed that penetration range by a considerable margin, which increases the risk for overpenetration. Plus, the WC typically has lower recoil, though I have seen some WC offerings that are loaded a little hotter, i.e. Buffalo Bore's 150gr hard cast WC; these would likely have more penetration than the typical target WC. I would probably choose a different bullet profile for reloads, though, as the short, flat WC profile doesn't lend itself to performing smooth reloads.
I will add that, technically, Buffalo Bore's standard pressure 158gr LSWCHP would be an option, but in my experience it shoots like +P, so I don't know if that would meet your needs.
However, my first choice for a .38 snubby load is the Speer 135gr Short-Barrel Gold Dot +P. It's what I keep in my 642. It's on the snappy side, but not what I would call uncontrollable. It's developed a pretty solid reputation in actual shootings and typically performs well in gel.
My second choice is the aforementioned standard pressure Buffalo Bore 158gr LSWCHP. Also known as the FBI load, it's been made by different manufacturers and, in general, has developed a solid reputation, too.