A treat for mice ? How about a candlelit cheese supper ?
I think a variety of attacks might suit you best, but poison works. Mind you if they go crawl away somewhere where you can't get them to die then you may find you have more flies next summer.
Or as you suggest the good old fashioned trap works, but you have to remove it afterwards. Bait it with a bit of chocolate.
I once got rid of two mice that had set up home in our house. I put a trap down (under the floorboards, 'cos that's where they were), and baited it with cheese. They weren't interested, so I baited it with rat poison - Warfarin, I think it was - and they went for it. Result: two dead mice.
I avoid mouse poison since it's usually a long-acting anticoagulants, such as Warfarin. While I have no sympathy for the nuisance little critters, they tend to go off and die under the floor or somewhere else inaccessible and stink for weeks.
Additionally, there is the issue of the poison's threat to pets and children.
I have good luck with a simple trap with peanut butter for bait...
A humane trap might be another consideration.
They need to be checked regularly (otherwise they're not humane anymore) and the live mouse must be released at least a couple of miles away, otherwise they will soon find their way back.
If you have a heavy infestation, then go for your last option.
A dear friend of ours used one of these, having caught a mouse and taking it down to the far end of the garden, we used to takes bets which one would be back in the kitchen first...quite often it was the mouse !!