Any load you put in any gun that will do what you need it to do when it comes to actually shooting a person will go through layers of drywall, and probably through a 2x4 to boot, at least in the thinner cross-section.
It has to, because otherwise, it won't penetrate the depth needed on the person you're hoping to never have to shoot.
Therefore, load an effective round in your .38, shoot at the person, not the wall, and don't miss.
An effective round is one that shoots to point of aim and penetrates 12-18" of flesh. Any decent loading should do that, from 110gr hollowpoints up to 158gr semiwadcutters. Personally, right now, all of my .38 Specials are loaded with 125gr Speer Gold Dots. But I could be just as happy with a SWC, or SWCHP, as long as it hits point of aim with the gun it's in.
The lighter hollowpoints may not penetrate as much, so if you're really worried about it, find a 110gr HP that hits your point of aim and forget about it.