It won't stress him too much, and if you're really worried, you can just put the container back in his viv when you're done and let him crawl out on his own. I powder the mouse bits I feed snakes that have regurged pretty heavily with Nutribac. Between that and the juice from cutting up the pinks into sections, the snakes are very slimy when they are done eating. I always run them under the kitchen faucet to rinse off, and have never had a problem. If they can do that, a little trip to and from the feeding container isn't going to upset them. I just find that I have much better luck getting a snake to feed if it is in a relatively small container, much less turned loose in the whole viv.
Think very small! (This is El Wray's baby feeding container. He'd been moved up to a Gladware before the regurge. Actually, he'd been moved up to a small Sterilite, and was confused, so he got down-sized to the Gladware. I just didn't want any arguements about eating multiple pieces, so I put him back in his deli).
You can do whatever you want- I'm just saying I've been through this before, and I am super conservative about regurge recovery, and I feel you'll get a better feeding response in a small feeding container. Covered with a dish towel, even.