This is another case where it would be nice to have your general location displayed in your profile so we would have an idea on your weather. Is it warm enough that those four week olds don't need supplemental heat? I assume the ten week old chicks are outside in the coop/run. Where are the 4 week old chicks? In the coop, in your house, or somewhere else? How big in feet or meters is your coop, how big in feet or meters is your run? I can't offer specific advice or make specific suggestions when I don't know what you are working with.
There are a lot of different things you could try. Sometimes this stuff is so easy you wonder what all the concern was. Sometimes chicks die. The more room you have the better your chances of success. It is often very helpful to house them where they can see each other but can't attack each other for at least a week or even more. A safe haven/panic room might come in handy. Wide separated feeding and watering stations are a good idea. It can be really helpful if they can get out of line of sight of each other. That could be by really having lots of room or by having places they can hide under, behind or over. Not trying to force them to be really close together, either by day or especially at night, can relieve a lot of stress on them. I don't know how you might implement any of these since I don't know what you are working with.
My definition of success in integration is that no one gets hurt. They can merge into one flock where they are all sitting around a campfire, making smores, and singing Cum Bah Lah together can come later when they all grow up. That moment comes when my youngest pullets start to lay. Until then I'm just happy when no one gets hurt.