Just like in a real estate transaction, brokers are there to hook up connections. Once the head-hunting is done, a lawyer or closing company takes over.
You can find buyer privately and hire a closing company to help... But sometimes these closing companies do not want to offend the big-3 and jeopardize their future referrals so I am not sure if they will accept your self-referred business.
Without a broker, there is no 10% commission to lose... if you wish, you can share 5% with your buyer so everyone is happy. It's like selling BLT for $100 for a $90 offered price.