Depends on your desires for your flock. Its my understanding that RIR typically start to lay in the 18-22 week range, which is pretty early, but not so early as 10 weeks. I'd expect noises from your cockerels before that date, but probably not consistently before week 16.
Personally, I'm breeding, looking to put some meat back on DP birds (together with other goals) - and have found 1 good young cockerel can easily cover a dozen birds+ with acceptable fertility rates in the eggs. And because I'm breeding, apart from excluding any obvious problems of coloration, my selection of males would be for size and earliness of maturity. By 12 weeks, I'd cull the two smallest for my table, and watch the last two - see who starts doing his duty first, and which of the two have the biggest size. Use that to make my final selection, and until then, I have a "back up" in case of disease, predation, or injury.
I'm guessing, reading between the lines, that is not the purpose (or perhaps, not the end) you desire for your birds. In which case, I'd suggest (if you have time and resources) setting up a second house and large run for a "bachelor flock".