My first time I waited till my new ones were similar size to old but after reading of the success of people doing it younger the last two times I did while still chicks. The first time at 7 weeks with their broody mum (they really went mum on her return, ignored the chick totally), recently at about 5 weeks from an incubator. It actually went easier than adding older birds. The others seemed to ignore them as part of the pecking order hierarchy battle because they were still chicks and so basically ignored them. By the time they do rate in their eyes as part of the pecking order they have been running with them so long they just all see them as already part of the flock but happily in their place at the bottom. The worst they ever got was a little chase away from treats when they got too cheeky.
BUT.....the ones you are introducing yours to are fairly young so not sure if they will react as calmly as adult birds sure of their place and I have a large run for them to keep out of every bodies way not a small portable coop setup. If you only have a very small coop setup I think adding anyone is going to be tricky because new birds need to be able to get away when needed. They also need to be able to go without heat, will a four week old be ready for that where you are? I'm heading into summer here so it wasn't a problem, if you are heading into winter it very well may be.
If you do add a chick, same rules apply as for older birds, let it be in the coop to be seen but seperate for at least a week.
When you add it have somewhere else for it to sleep safely seperate from them till that night you go to lock them up and find it perched with the others.
Make sure there is food and water at both ends of the run in case they won't share.
Put some safe hide spots in there so it has somewhere to hide or escape if they do chase it. I sat things in there at chick height for it to run under but that the big birds couldn't fit below.
I also agree with above, if you can add two I'd do that because being the odd one out is a lonely place.
Oh and I'd get rid of the rooster first. And the others won't get stressed, I don't think mine even noticed ours was gone when neighbours complained and we had to Rehome him...