i think mice are very cute, but the sight of them covered in oil made my skin crawl for some reason and i would never keep them as pets (unless i had a lot of snakes/owls/etc to feed)... as a kid i had hamsters and that was enough pet rodents for this life time.
i use snap traps with peanut butter and once in a while we've set up buckets with sunflower seeds on ramps and in the bucket floating on the water to catch chipmunks and there will sometimes be a few mice in there. i don't want them as pets i just want to keep them from getting into the walls of the house and garden shed.
a good use for used vegetable oil instead of throwing it away. except we don't really cook that ways now and barely.
i wonder if you could use about any oil at all and bait it just a little with sunflower seeds or just a few dabs of peanut butter around the inside of the bowl. the mice seem to really love those... i know they can smell even microscopic amounts of peanut butter because i can catch them in traps that have had all the peanut butter licked off them and for months afterwards.