Would you let your cat eat the mouse? (Active situation) Help please?

So I went get my cat some food and when I opened the cabinet, a mouse sped out from inside. My cat immediately grabbed the mouse and brought it nearby me. Then he dropped the mouse and it is now hiding behind a bookshelf and draperies. After grabbing a wad of paper towels, I sealed off the room and searched for the mouse with a flashlight. When I found the mouse in the curtains, IT MADE EYE CONTACT WITH ME.
The problem is that my sweet cat rubbed against my leg as though I was helping him hunt this mouse. My true intention was to catch it in the paper towels and let it out.
So now I’m torn because the mouse looked at me desperately and my cat thinks I’m helping him hunt a mouse.

I don’t know what to do. It is past 11 pm. I need to go to bed. But I can’t sleep knowing there’s a mouse on the loose. AND I would feel terrible to wake up to a mouse massacre.

Do I just keep the door closed and let nature take its course? I’m sad even thinking about it.

(Obviously I know that a mouse inside is a problem and I’m already working on the solution to that.)

I already know that I’m ridiculous when it comes to animals so you don’t need to tell me that.
Would you let your cat eat the mouse? (Active situation) Help please?
Would you let your cat eat the mouse? (Active situation) Help please?
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Update… I just couldn’t close the door on this situation. I tore apart the room and caught the mouse in my wad of paper towels. I could feel how hard he was breathing through the layers of paper towel!

I rewarded my sweet kitty cat with some treats. He’s lived a charmed, indoor life and although he may have enjoyed eating that mouse, I could not let that unfold inside of the house.
Would you let your cat eat the mouse? (Active situation) Help please?
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