Disclaimer: IANA pest control expert. However, in my time I have dealt with both mice and wasps co-habiting with me.
Having neither wasps nor mice is contingent on “cleanliness”. The most immaculate homes can end up with mice and wasp problems. It’s just that those particular houses at that particular time and place happened to offer optimal habitat for those particular animals, and in they came.
There are any number of designs for humane mouse traps available; google “humane mouse trap” or “humane mouse control”. However, if the extent of your problem is such that you can hear little mousey feet running around in your walls at night, you have too many mice for traps to be effective–you have, IOW, an entire functioning colony of mice–and IMO you’re going to need to call in a professional exterminator, and yeah, mice are probably going to die. You can ask him to use humane traps, but then the problem of where he’s going to dump those captured mice arises: anywhere he puts them, they’re going to die. They’ve got a predator-free environment in your home, which is why they’re there. But if he, or you, dumps them in the nearby state forest, or farmland, there they are in the thick of things, with predators all around.
And if you just take them out in the yard, they’ll be back in the house by bedtime. They were out there originally, remember, and they know perfectly well how to get back inside.
Bear in mind that, whatever method you use, if you do manage, slowly but surely, to capture the adults foraging out in your kitchen, you’ll be leaving juveniles to starve, back in the nests in the walls. There isn’t any way to “persuade” a colony of mice to pack up Grandma and kids and move out.
Those ultrasonic rodent repellers do not work; don’t give money to any exterminator who promises to solve your mouse problem humanely by setting up one of those.
Setting out a few mouse traps yourself in my experience works only when you have one or two tentative residents checking out the premises, not an entire breeding colony.
Next, you need to consider whether the little mousey feet you’re hearing in the walls are indeed mice, and not rats. Rats are also not contingent upon “cleanliness”; they will also colonize perfectly clean human homes. Can you also hear gnawing sounds coming from the walls? What size are the droppings that are being left?
Question: Would you care about humane removal if they proved to be rats and not mice?
Removing wasps humanely is quite simple: all you do is knock down or otherwise destroy their nest, and then every time they start to rebuild it, knock it down again. Eventually they will get the hint and disappear. But you’ll have to watch that space every year, because if it offered prime habitat to wasps one year, it’ll continue to appear tempting to new colonizers.
You could wait until next winter when the colony normally declines to only the queen wasp, but then you’d be definitely killing her, because in the winter she wouldn’t have anywhere else to go.
You are also on your own as to how you destroy their nest without suffering multiple wasp trauma.
My dad used to stand on a ladder and use a really long stick to whack the nest that appeared under our eaves every spring–took one well-aimed hit, and then hustled back down the ladder and indoors for half an hour.