Yep, keeping one of the roosters might work if you can keep him quiet. I have not heard of the zapping collar and like you, think that sounds a bit mean and not something I would consider. I am in a no rooster zone and prefer not to draw attention to myself and my chickens by trying to bend the rules.
There is the no crow collar which does not zap them but reportedly restricts the crowing by not allowing them to draw in the required amount to crow loudly. Again, I have good and bad news regarding the no crow collars:
They work on some roosters, not on others.
They can take some tweaking to get right and this can take a couple of weeks.
There is a choking hazard.
I have a friend who tried one on her first rooster and even with the collar as tight as was safe, he still had to sleep in a container in a dark area with the collar on to stop him being heard. She ended up rehoming him because she felt mean. She kept one of his sons and the collar works fine on him, keeps his crow very quiet and he gets to sleep on the roost with his gals.
BUT with her first rooster, she nearly lost him during the ‘tweaking’ period as he started to choke, get dizzy etc.
If you keep one of the boys just until she is old enough or ready to be integrated, is there any way you can darken the mini coop to confuse him as to the time of day and deter his crowing?
Maybe have a trial run with your lone hen and the big girls on free range? See how they go, as you say, they might be OK with her. I would keep the boys locked up though.
