Sorry to be the bearer of bad news, but I’d think again.
A cockerel starts crowing at 5am and often earlier, even in the middle of winter with its longer nights. And yes, that bothers many people, and unless you’re in a rural area the council will likely take the complainers’ side. It’s not the sound, it’s the timing.
Just imagine someone wakes your whole household up by ringing the doorbell at 5am (let’s call this the urban equivalent of a cockerel),
then again half an hour later, and again and again. Every single day... Having your cockerel at the other end of the field won’t resolve the noise issue unless your field is miles long.
But say you go ahead and start breeding, inevitably you’ll be hatching boys. Apart from needing to know how to humanely despatch them (lovely rehoming stories such as doganjo’s above are very far and few between, unfortunately), within a few months those young boys will crow, too, long before they are ready for the table if that’s a route you’re considering.
And before you know it, lo and behold at 4am every day there’s The Great British Crow Off taking place in your field. Oops...
Neighbours requesting you to not be noisy until 9am I can sort of understand, I’m up early so my cut-off point would be more like 8am (need to allow for ample time with tea and coffee before I can face the incivility of the wider world), but try explaining that to a cockerel. And any chicken coop, no matter how dark, will still allow the sound of crowing out - it needs plenty of air holes, after all!
So I’d say you’d better not. Crowing comes naturally to a cockerel, I’ve heard of other ways to try and stop it, all of which sound cruel. I’d try and deal with the trespassers, maybe electric fencing? Or using heras panels for the run? You can pick those up cheaply, we built a massive and very secure run with them.
I do keep a cockerel, btw, lovely gentleman, he has fathered lots of chicks over the years. Hence why we know about the pre-dawn crow offs...
There’s absolutely no way I’d have him anywhere near my bedroom window