“Alpha males need people they can dominate. Sigma males are a entirely different breed of cat.”
I’ve always considered myself an alpha male. When a situation develops where a leader is needed, usually in the workplace, I waited until it was obvious no one would step up. Then I took over. If there was a titular manager, who had no clue, then I’d say things like, “Do you think we ought to run an endurance test to determine whether the product has a high failure rate?” They invariably would agree as whatever I suggested was a good path forward. I do not want to lead, but I won’t be part of just foundering around and not succeeding.
I was as successful in my working career as much as management would allow. I have been far more successful since retirement as my present business is my fourth company. Am I a sigma? Maybe. But the vast majority of my male friends are alpha males. We get along great. I don’t feel dominated, nor do I dominate.
On top of that, you sound like the perfect kind of leader...one who doesn't want to lead or be a leader but will do so because you feel a sense of obligation to do the right thing.