I just hope you do not stink. :) Another note: perhaps you could only clean your underarms to reduce the (possible) smell and leave everything else intact (if you do not hang around your arms raised, that should be a good strategy).

Full disclosure: I actually do use the same strategy, just put soap/shampoo on the smelly parts (and hair in my case as I do not stand oily hair) and leave everything else untouched. As for anecdotal proof, I do get less bites as the rest of the family.