Follow up: gave her a bit of a soak in some warm water with a little Epsom salt. A lot of the poop came off and I just wiped off the rest. Her vent looks fine. She's pooping normally and her butt is still clean today.
She didn't react badly. The dimmed lights helped because she couldn't really see around her to find a place to escape to. She just sat there looking confused and then kind of resigned herself to the situation. Other than my bathroom smelling a like wet chicken for a bit, it was a success.
I played a little Laurence Juber for her, too, I like to think he helped us both out.
That song is called "Snowflake In My Pocket." I had the pleasure of meeting Juber several years ago at a conference. In addition to being very talented, he's quite down to earth and gracious, and he told us the story behind the title.
His little daughter had a hamster named Snowflake who disappeared one day. She was understandably upset so he drove to a pet store to get her another hamster. He laid his jacket on the seat next to him in the car. As he drove, he noticed something in his jacket was moving. He pulled over and looked in the jacket pocket and there was Snowflake! His daughter was happy and a song was born.