Depending on how many mice (if you know?) that you have coming and going, all these `professionals` would do would lift some floorboards and place traps and small bags of warfarin (a blood thinner) down. Warfarin thins the blood and is also used in human medicine (controlled) to patients who have had strokes or are at risk of clots. So basically, the mice die from an overdose of this and I can`t see it being a quick death but a low, prolonged one.
Trap devices would be quick, but only if they trap the full body and not a limb or a tail.
I would still advise blocking any entry holes in the building and keep foodstuff well out of reach. Most houses have mice and unless they are really a nuisance, they learn to come and go without actually staying in one place. I`ve had a few get into the actual house, but mostly they run a mile if spotted and the majority will stay hidden and only come out at night mostly to look for food.
You either learn to live with a few mice or you just can`t stand the thought of them being around, so it`s never an easy decision, but unless they are proving a real issue like getting into food cupboards or you are actually seeing the mice in the rooms of your house, I would carry on with the humane traps and scatter some millet/hamster food inside. Using humane traps does mean re-releasing, but at least what you find in the trap will be a little face staring back at you and not a mangled one! Mice will learn to come back to the same feeding station over a night time if they know there is food left out.