Us babies don't have body hair. Well I don't want to anyway. Face and armpits: about twice a week. Nether regions: about once a week. Arms and legs: when I get round to it. Bare is more babyish, which for me matters. Also, hair in damp places makes a good home for bacteria, hence smells. Just washing doesn't shift the little critters, so shaving is my solution to that too.
Unfortunately, I believe this is common in the medical field. About the only thing that i think can work is to have an answering machine take the call for screening.