I'm guessing OP is considering promoting his employee to a level where he would have to interact with clients and officials more. His neckmuff is clearly going to cause some problems there.
While I don't know the specifics, I don't believe I'd promote him. He's clearly very competent where he is, and if he isn't presenting himself in a way that would impress clients, he shouldn't be in a position where he's interacting with them.
I mean, you have someone who is thriving in his current position, and you want to move him up to one where he's clearly going to make other employees (and potentially clients) uncomfortable?
Do NOT, under any circumstances, bring up his appearance. You have a good employee. Don't make him uncomfortable, as it will impact performance.
A small percentage?
Last I checked, the entire tech industry, which is pretty much the only thing keeping america relevant, doesnt usually give a shit about that.
Tech industry here! When I meet with clients or demo a product for the CEO, you bet your ass I'm not going to come in wearing flipflops.