What I did for my last batch was to set up a cat carrier in a circle of chicken wire within the yard of the existing chickens. This way, they can interact all they want, but nobody gets hurt. Left that like that for a few days, then ended up moving the cat carrier into the base of the coop at night with the door clamped open slightly (open enough for the chicks to get in and out, but not open enough for the big girls to get in) and let them all wake up together. For a while, there was two distinct flocks in my yard, but over time they became one.
But yea, for age, I'd agree with the others at about 4-6 weeks. Personally, I play things more by how well the birds are feathering out and the weather in the area. Fully feathered bird and 70F outside? Time to stop stinking up my house and go outside!
There is an interesting side dynamic with your particular setup that has me curious. It's said that when you introduce chicks, you introduce them in a group so they divide up the abuse they will take from the older ones. Your particular situation will see a flood of 20 newbies against the 4 existing. Due to the sheer numbers, you may see a complete flip in pecking order with your newbies picking on your existing flock. If this happens, it may be worth a re-introduction where you introduce the newbies something like 5 at a time per day.