I, too, don't make decisions based on what is expected by others. I agree that if you don't mind if he has his binky then you don't need to worry about it. I doubt that any kid started school with his binky. lol
But if you want to break the habit I think it has to be done cold turkey. Does he have anything else, like a blanket, that is security for him? He has to have a security object. My grandson adopted a stuffed duck for his after he lost his binky.
Here are some ideas that I've heard. To put all of his binkies in a sack or box and say that you want to give these binkies to a really small baby who needs them. He's a big boy now. Talk about doing this and enlist his help in gathering them up and packaging them. It's a variation of what worked with your daughter. Then take them out of the house and do what ever you want with them.
(I have found that thrift and resale stores will not accept them.)
You could have a going away party for them.
You could have him help you throw them away after a few days build up. Emphasize that he's a big boy now. You know it's hard to give up your binky but it's necessary so that your teeth grow in straight.
If he hasn't had his first dental visit you could take him to the dentist and enlist the dentist's help in removing the binkies.
You could tell him that all binkies have to be out of the house by a certain date and then take them out of the house on that date. If he's teary and wants them back, hold him and tell him you know that he misses his binky. It's OK to cry.
If he doesn't already have a lovey be sure to provide a chance for him to find another one. He or you might choose one from the house as my daughter did. HIs mother just kept giving the duck to him instead of the binky when he went to bed and it became his lovey. Or, perhaps trade the binkies for something else new. He could pick the something else. Take him to the store and tell him he can pick out a stuffed animal or one of those small blankets with a stuffed animal head attached to it to take to bed since he won't have the binky anymore. That you understand that he needs something to help him get to sleep and this can be that something now that the binky is gone.
Whatever you decide to do be sure to include your son in it. The binky is important to him and can't just disappear. He will accept it better if he's involved. He'll still want it back for awhile. There will be a griefing period.
And be sure that you get all the binkies from his grandmother's house. Enlist her support in getting rid of the binkies. If she "sneaks" them in once they're gone from your house, he'll be confused. As it is now with her connecting the binkie to bed time it's probably not so confusing because it's close enough to what you do.