This pops up all the time and it's a tough situation. Most would say cull him as you do not want to pass on aggressive genes. To me that is a last resort option. Also I've observed that a lot of people who fight back with their roosters just wind up escalating the fight and aggression from the rooster.
I had one of my Buff O roosters peck me hard the other day. They are 13 weeks old and this one in particular has matured faster than the other roos in the flock. I was petting one of the hens and he didn't like it. True, he was protecting the hen, good on him, but bad also. You don't fool around with the flock mistress, namely me. Before he had time to react, I pushed the hen aside and scoopted him up. He hates being held, but I tell ya, for me, this strategy has really worked. A moody rooster gets held until he stops struggling, then I hold him and walk around with him in my arms for at least 5 minutes. If he acts up again, he gets carried around longer. Once they stay quiet for 5 minutes, I put them on the ground and do a dominate down with them, namely, they get pushed to the ground like they would do a hen when they mount and held there once again until they stop struggling. I pick them up again and hold them until they stop struggleing. Once they are quiet for a few minutes, they get sent back to fht flock.
So far no more trouble from Mr Red.
We have 5 roosters and I have had to do this to two of them. The other 3 are sweeties.
If you can't pick him up, I'd try using super soaker squirt gun or garden hose on full blast on him.
Cull him only if you can't establish yourself as flock master or mistress and get him to respect you. But you have to get him to respect you and you him. In his mind he is doing his job, especially with the dogs, which is good. He just has to learn that he cannot attack people.