I know the command "showracemenu" lets you redo character creation, but I heard it also resets your stats. I definitely don't want to change my race or reset my stats, I was just hoping I could tweak my characters hair color without changing anything else about him. Is it possible?

No, the only way is showracemenu. But as long as you don't change the race, and only the physical appearance, then the only thing that should change is the magicka/health/stamina, which is easily fixable with the console.

I used showracemenu routinely without changing race/gender, and my stats have never been affected by it. I believe it's ONLY if you change race that happens.

*dittos what Ryu said....*

The showracemenu command has never messed with my stats, but on occasion it has removed my racial bonus from Active Effects--which is easy enough to add back with the console.

Not even that. You just need to save and restart the game. It will be automatically added back.