This particular mouse at Stony Brook Shelter seemed to have been blind although it looked very healthy. Stumbling into the shelter after a long night hike, it was licking rusty nails as though testing for food as I held the headlight in it's direction, but I don't think it noticed the light.
Personally, I wouldn't kill the mice at the shelters, but some hikers do. If hikers are careful hanging their food and unzipping their gears, they should survive most nights without damage. Luckily, I had no gear damage while staying at a few shelters.
Kung Fu and I stayed at William Penn shelter one night, and there was a cute baby mouse residing there. Kung Fu asked if I had a mouse trap, and my reply, "No, I was going to let the mouse be." A few minutes later when he saw it, he said he had a mouse trap, and it seemed for a moment he was going to fetch it, but then he stopped to my silent relief. Maybe he recalled my answer earlier and felt guilty.
(I wanted to stay alone in the shelter as usual, but it turned out Kung Fu was a cool shelter mate. We ended up staying at 3 other shelters and the jailhouse hostel together throughout the trail.)
I think his better mouse trap was left in the hiker's box at the Hiker's Hostel in Glencliff, New Hampshire. Or at least I think it was his mouse trap I saw at William Penn shelter.
On a tangent, the next morning at William Penn shelter he gave me a pair of Oakley sunglasses he found. They appeared expensive, maybe 100 bucks, but I promptly scratched them heading into Palmerton, Pennsylvania.