If I were to have absolutely no choice but to carry a 22 for defense, I'd choose the ammo based on two criteria...reliability and performance.
Reliability: Rimfire ammo is notorious for having priming material unevenly distributed around the rim, especially with bulk stuff, and that can lead to clicks instead of bangs. The wax lube used on many styles also tend to pick up lint, dust, and other contaminates which can cause issues. And finally, most rimfire is not very water- or moisture- proof. I would look for a round with a plated bullet or a dry lube in a box which separates the cartridges from one another so they don't get banged around, and which has the minimum bullet/case play (indicating a robust crimp).
Performance: Fact is, the 22 has the highest incidence of "failure to stop" of any cartridge currently in use, regardless of velocity or bullet style, so choosing a round that operates 100% of the time, hits to the sights, and uses a bullet of sufficient weight or design to reach vitals is most important. Flat nosed bullets do more damage than round nose, and most guns with fixed sights shoot to POA with 38-40 grain bullets, so I usually recommend the CCI SGB or Velocitor (despite being an HP, it has a flatter nose profile than many). Apparently Federal agrees with me about flat-nosed slugs, and developed the Punch, but decided to go with a non-standard case length and lightweight bullet which keeps it from being one of my top choices.
I would not bother to alternate, as even 22 HPs which expand are not going to "shock and stop" bad guys. Watch enough bodycam video and it becomes apparent that even well-performing 9mm, 40 S&W, and 45 ACP don't do that very often with anything less than perfect placement.