Absolutely shave it, with clippers or a razor if you want to go all out I use clippers with no guard. My brother's mates ask him things like "does your brother shave his head or is it like that naturally". I, of course, thought this was insane but I realized people just aren't as observant or bothered about it as you are.
Every normal man must be tempted, at times, to spit upon his hands, hoist the black flag, and begin slitting throats. - H L Mencken