I love this description from Wikipedia: "It was originally designed as a black powder cartridge. The .32 S&W was offered to the public as a light defense cartridge for "card table" distances."
Light defense.
Card table distance.
https://en.wikipedia.org/wiki/.32_S%26W
Look, it's a black powder round. Small caliber. So, low pressure, small bullet at low velocity. Not much energy. Roughly 85 grain bullet, subsonic, perhaps 85 ftlbs ME. So, just a bit BELOW a .22 LR. Not even close to a .22 Magnum.
At that velocity, with that diameter, bullet design really isn't going to matter. You're not going to get expansion, you're just hoping for penetration. Hoping...
Notably, this is the round that was used to shoot President Mckinley. Shot twice, he succumbed to sepsis 8 days after the shooting.
Not exactly a man-stopper. It's lethal, eventually...maybe...though, with modern medicine, which McKinley didn't have, it may not even be lethal unless you get very lucky.
So, Lead Round Nose, or Wadcutter, either one is as good as it's going to get.
What you've got is a cool old gun. You should enjoy owning it and shooting it.
If you honestly want a decent defensive gun, you should really consider something different. It could still be cool and old... but even a .38 SPL is a huge step up in power and effectiveness...and anything in .45 Colt (Long Colt, like the Single Action Army) will have the power (velocity, bullet weight, bullet diameter) to be effective in a defensive scenario.