One thing that works really well for a lot of dementia caregivers is turning handwashing into a routine that happens automatically after every bathroom trip rather than making it feel like a reminder or correction. Something as simple as placing a really nice smelling soap right next to the sink at eye level can trigger the habit on its own without you having to say anything. If that doesn't work, casually washing your own hands at the same time and narrating it out loud like "oh let me wash my hands real quick" often gets them to follow along naturally without feeling singled out.
I got my references here:
https://hopebridge.care/navigating-hygiene-concerns-with-elderly-parents/
https://en.wikipedia.org/wiki/Dementia
https://www.betterhealth.vic.gov.au/health/conditionsandtreatments/dementia-hygiene