My son got his first haircut at 3 months.
Maybe ask the stylist to cut his hair with scissors instead of clippers. If he is going to do clippers, then have them show him the clippers (turn on and off) so he can get used to the noise, intead of going straight for his head. or let him see someone (daddy, uncle, etc) get their hair cut first.
Plus, they gave my son a lollipop to eat while he was getting his hair cut. For some odd reason the lollipop kept him preoccupied. Take a blow pop with you just in case they don't have one.