What do you have in mind when you say medical device? Automatic defibrillators, glucometers, other automated/electronic medical equipment? Lots of EE and some MEs there.
How about gastric tubes, dialysis microfiltration, intraocular lenses? (All those BabyBoomers getting their cataracts removed, you know.) Might want an ME, ChE or polymer chemist for the first, likely a polymer chemist for the second, and chemist and/or physicist for the last.
How about surgical equipment and orthopaedic fixation devices? MD, ME, maybe biomedical science (whatever that is?).
Sorry, I'm just shooting in the dark here. If you have some specific companies in mind, you can check OED (link below) to see who works there in-house, and check their patents at the patent office to see what firms do their work. If you get really lucky and the firm allows individual attorneys to list their names on the patents, their firm biographies will normally tell you some of their technical background.
https://oedci.uspto.gov/OEDCI/