Here's the Yang to Suzies' Ying, or however it goes -she and I represent both ends of the mamasource spectrum- :)
A consequence for the behavior will teach him quickly not to do it. Words alone often don't click with one year olds. God bless the parents with kids who stopped with just "no", or with he patience to put up with the behavior or do endless time outs or situation removal.
If you give 1 calm warning and then on the second warning give a swat on the butt (upper thigh, below diaper-or maybe back of his hand since he's using his hand to pinch). He'll stop. He won't want the consequence, so once it clicks (doesn't take long, kids are very smart) he'll decide to stop the behavior when he hears you say no. Of course you don't want to hurt him, but it has to sting or he won't care.
Don't wait until you've said no 7 times, or he wont' react until you say no 7 times. Be consistent, or he'll gamble for the times he gets nothing or a cushy time out. Be calm in your tone, or he'll think the consequence is a result of your hysterics, not his action and he'll be confused.
If he knows he ALWAYS gets a consequence worth avoiding for pinching etc. be it a person, an animal -whatever-after one or two warnings, he'll decide to stop doing it after your warning, and learn that no from you means no for other things as well.
My son bit me twice HARD at one year old, not doing anything wrong or mean, just trying his choppers. He got two swats two different times after being warned calmly, no anger, and hasn't bitten anyone again at 18 months old. I caught him with his mouth wide open behind his sister's shoulder, and said "no" calmly and he closed his mouth and walked away and got big hugs and kisses. My daughter never bit, she knew "no" before the urge came up, so when she bit her papa once, at 18 months, he said "no" and no consequence was necessary, she never has tried to bite anyone else. But she did know already by that age that warnings meant consequences so she responded to verbal requests.
Your little guy sounds pretty used to having fun pinching, so it may take a little longer, be consistent if you choose this method-good luck whatever you choose!