Football, boxing... seem the top two to cross off. I think skiing is perhaps the third to cross off.
At least with skiing, getting hit in the head isn't the point.
Wait until you hear about shinty.
Have you ever seen ice hockey? Okay well imagine that if it was on a field and if you made it into a really fast and violent contact sport.
Skiing is pretty awesome and IMO risk of concussion or serious injury is very low if you are not a freestyle or extremely aggressive/risky skier.
Football and boxing involve guaranteed sub-concussion head impacts every session and likely full concussions at least a few times a year.