What's the most usual way to say "hand sanitizer" in Chinese?
If you want to say hand soap (not necessarily for sanitation), you can use 洗手液. To specifically ask for hand sanitizer (for disinfection/sterilization), you may want to use 消毒洗手液. Below is an analysis for the options you've listed.


  洗手液 xǐshǒu yè


(Liquid) hand soap. Here soap is in general sense, could be sanitizer, scented soap, skin smoother, etc.


  洗手 xǐshǒu


(Verb phrase) to wash hand


  免洗洗手液 miǎn xǐ xǐshǒu yè


Waterless hand soap. Though not explicitly stated in the name, the waterless hand soap products are mostly sanitizers.


  消毒洗手液 xiāodú xǐshǒu yè


Hand sanitizer. (消毒 means to sterilize.)


  ___的洗手液 de xǐshǒu yè


(Incomplete phrase) hand soap of _