1) home health aid
2) phlebotomy
3) radiology technician
4) intakes in homeless shelters (taking vitals, interviewing, assessing hygiene)
5) volunteering in a NICU (neonatal intensive care unit - holding and caring for newborns, talking with families, etc)
6) mental health counselor (psych ER, inpatient psych) I've heard there are bachelor's level people who do this
7) dental assistant

9) hospice volunteer
I think for a lot of these, though you wouldn't be hired as a health care worker (homeless shelter worker, for example), you could pretty easily make the argument that you work with patients - helping them clean themselves, get fed, monitor their level of functioning (diet, behavior, etc.), and interviewing. These are medical skills, as I see it.