I doubt it. If you had some kind of open wound--like a compound fracture--I'd be more concerned. The accounts I've heard and read of people getting sick seem to be the result of part or all of a wing being amputated, which would provide an easy way for germs to enter the body.

[Yep, he's not about to make any fancy claims about the wings until he gains a better understanding of their structure. As far as he's concerned, they're just another set of limbs--limbs with a very high number of nerve endings, yes, but nothing really beyond that.]