I believe all things should be done decently and in order and God is pleased in that.
Secondly, I believe that the ordinance of baptism is given to the local church and not individuals. Therefore if one is not there who has been given the authority by the local church to baptize I would not baptize. Remember the thief on the cross was not baptized. I don't believe he would lose any reward for not being baptized or you would lose any reward for not baptizing him.
I wasn't baptized until two years after I was saved. I never doubted my salvation. I was mixed up in an interdenominational organization that never stressed the necessity of baptism and therefore was never brought up as anything that one needed to pay attention to. I wasn't even a member of a local church during that period of time.
Benjamin got bent out of shape when I asked the question "From whom did you receive permission to baptize?"
You have hit on the answer: First, decently and in order. Second, it's an ordinance given to the church, not individuals.
What happens if you have more than one person who wants to baptize a new convert? What if a member simply gets up and says "I wanna dunk him." Another says "Naw, I wanna do it."
The first guy walks up the steps down into the baptistry, pushes the pastor out of the way, graves the baptizee by the scruff of the neck and pushes him under (saying the proper words at the same time).
The pastor floats to the surface, sputters and spits and says "What in the world are you doing!!?"
The first guy says, "why, I'm exercising my right as a believer to baptize. Jesus gave me the right."
The second guy arrives at the baptistry and he's not happy. He wanted to baptize, but the first guy outmaneuvered him and got there first. "I'm gonna do the next one, so step aside."
Now, I made this up to make DHK's point of decency and order. For order's sake, somebody has to decide. Nobody would really do this, would they? Benjamin?
The other point is, by claiming Jesus' Commission as your authority to baptize, you have conceded the necessity of authority. Now, we'll argue from whom the authority comes.