I have to warn you all that of you give lo scissors (even pretend ones) to "cut" hair of a doll or toy....be prepared to hide ALL scissors until they are older, because they WILL cut their own hair when you're not looking.
There are a few ways to keep a lo distracted. I no longer do children at my salon, but giving them my squirt bottle worked like a charm almost every time. I'd ask them to squirt my comb or my palm so I could wet the hair....they didn't mind as much when they could use the bottle! Also I'd put a towel on top of my station and ask them to squirt the towel as much as they wanted.
Lollipops are incredible for a lo who doesn't regularly have them.
You might be surprised at how well your lo might sit for someone other than Mommy!
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Especially if you visit* first....slip the stylist a sticker or a treat to *give* your lo, then leave. Next time he can sit in the chair...(or not).....but pay a few visits to get him acclimated, wait a week in between...just stop by and say hi, kwim?
Cut the part that bothers you most first...bangs, ear area....that way if he freaks out, the bothersome part is done.
Dont forget that little ears fold...fold them forward with one hand while you cut around the ear with the other hand.
If all else fails....asleep in the carseat has worked!
HTH!!