You only have one rooster. You can only get one hen. I don't understand that but I don't have to. Those are the boundaries you have set.
How old is he, by the way. Might have some suggestions a to what to look for age-wise. I'd suggest staying in the same maturity level.
People bring home chickens from swaps and auctions, they take chickens to shows and bring them back home. Bad things can happen but that doesn't mean they always will. It is possible you could bring home something that would kill him, but pretty unlikely. You might bring home something that is an inconvenience but that can be treated. You may have no problems at all. No matter where you get a chicken there is some level of risks. Swaps and auctions are more of a risk than some other ways.
You are in Texas. You might try finding an active Texas thread in the "Where am I? Where are you!" section of this forum and chat with your neighbors.
My first call would be to your county extension office. Tell them what you are after. They may know of a chicken swap or livestock auction that has chickens in your area. Or even better, they may know of someone that could sell you a chicken. They should know a lot of farmers.
You can talk to people at the feed store. They might know someone that can help or they might have a bulletin board where you could put a notice.