I don't think you are being irrational. Truthfully, being handed a snake and picking one up on your own are two totally different things. I've handled lots of snake over my lifetime, all handed to me or placed on me by the owner.
When it came time to hold my own, I was very nervous. Not so much of being bitten, but that I would hurt her. I had to try three or four times before I took a deep breath, gritted my teeth and picked her up. Know what happened ? Not a darn thing. After that first time it was easy, and I'll even pick up unfamiliar snakes with permission.
So your best bet is to realize being nervous is normal, you already know a bite is not likely, and if you did get bitten it won't hurt, so take a deep breath and just reach in and pick him up. Once you do it the first time, you'll forget you were ever scared.
Gale