SHELTER, this is probably the toughest of the three things I mentioned, as they like the same type places that we do.  It is a good idea to block any access that they may have by plugging access points to your shop if possible with steel wool, mortar, ect.  

WATER, this is also pretty difficult as the little critters can survive of the persperation from cold water pipes among other things, but elimination of standing water that they can get at doesn't hurt.  

FOOD, this is usually a little easier, while you may not be able to eliminate sources outside, good hygene in the shop and areas can reduce the food supply and make it more likely that they will eat any bate, or approach any bated traps that you put out.  (who will chew on wood when steak is readily available)  

The problem is that the little turds are careful enough that they can steal the peanut butter from the trigger without setting it off.

Do this and they won't be able to get it of without setting it off.

Load the trigger with the peanut butter and then take a small scrap of paper towel and knead it into the peanut butter. Make sure it gets in there good and soaks up good.  Then set the trigger and place the trap.

The mouse will not be able to get the peanut better through the paper towel without setting off the trigger.

Very effective!

http://www.homepower.com/files/electricfence.pdf?search=electric%20fence

25,000 volts ahould be enough to put it in low earth orbit!

Make sure the wife does not touch it by mistake, or you may go into outer space.

Shop online or feed supply for windup repeater traps.

If you can keep pets and childern away, hard to beat the
sweet taste temptaion of anti freeze as plain liguid or soaked
in something that can be tossed in hidden spaces.

In pack rat territory they store cars with glove box open
and hood bricked up a few inches or they feel secure
enough to nest and enjoy wire insulation snacks.

In a city home had actually rats move in so tried clap traps
but they set em off then eat the bait, so I got 'trickier
and trickier' until last mechanical attempt had 5 gal bucket
by a bench so they could only jump to get the bait barely
suspended on separated layer of toilet tissue to make em
miss step and not see the bottom fully covered
in set traps... I slipped once, ok twice and set a trap off
which set em all off, barely escaping myself yet on next
AM each trap was sprung and no food or rat in bucket : (

Mice can't climb well in a metal container, glass, porcilain, etc.. and especailly if wet.
If you don't want to drownd them, use such type of large container with a little water in bottom to keep their feet wet, if you do want to drowned them use about 6" of water.
 Set container where they can walk up to it and fall in, set bait in some way to attracked them to crawl into it.

Under counter or shop table maybe hang a string that lowers into the container about even with the top or a little below the top and bait end of string, so they have to strech to reach for it, plop they fall in and are trapped.
 A metal bucket, an old deep kitchen sink, glass gallon jar, etc... should work well, just make it easy for them to get to the top of it, like a ramp or set it next to a shelf about same height.

You could also use a trap door type system. Make a ramp for them to run up and across the top of the container from one side only, put bait on other side, small sectoin of ramp over the bucket is hinged with a loose spring so their body weight causes it to drop as they walk acrossed it to get to the bait. Mouse falls into bucket and ramp raises for the next mouse to try.

I have found mice fallen into kicthen sinks and trapped, like when the trap froze in an unused house and the sink would not drain, mouse fell in and was trapped. Also I think same house I found one in a toliet, same thing fell in and trapped. Mice also cannot jump very high when wet to get out of such a trap, and also not jump at all if in about 6" of water.

How you want to get rid of live mice then? Feed to cat. Don't like cats? Get a pet Snake :)
 Maybe dump them off as you drive by a wooded area in the middle of nowhere far from home.

Another mice catching trick is to hinge the lid on a can, cut it to be maybe 1/2" short of reaching to the bottom when can is laid on side. Fasten can so it cannot rollover. Place bait inside at the solid end of can. Mouse will look it over well and feel it is safe, then pushes it's way into the can raising the hinged lid as it crawls by, the lid drops and mouse is trapped inside. You'll need to fix the lid so it can only push into the can and not outwards away from the can, a simple pin works or mount it to a board with the hole in board cut smaller then the lid.
 Reason you want the bottom edge of lid a bit short is so mouse can see under it and inside the can, but do not make it short enought he can crawl back out under it.
 To release the mouse turn can over so lid falls inside and and sit it down so mouse can crawl out or dump him out.
 Can trap cna be reused as often as wanted if you remove the live mice, but if you let them die in the can it makes a smell that stops other mice from entering latter.
 Cans are free so make as many as needed when ever you need them, just eat lots of food in large cans.
 Manwich, Spaghetie sauce, large juice cans etc.. Wash them out and put peanut butter in there.
.
nothing to lose

 Back when i was doing the poisonings i never saw a dead mouse from it but a stray cat showed up for a couple days.

My wife and I moved in with my dear aged grandfather, who had the worst mouse problem I ever saw.  After going through legs chewed off in snap traps, missing traps, glue traps, and mice with nothing but there bellies caught in the trap (had to beat that one to death :(, I knew there had to be a better way.

My solution: 4 steel catch'em live type traps with peanut butter crackers inside. Now I was not in merciful mood at this point, fellas, and it was never my intention to let the wee tim'rous sleekit beasties go free.  That being said, I found a nice cardboard box that just fit the reusable traps.  I stacked the traps in the box and sealed the box with packaging tape.  Low on time, and the next four-legged wave moving in as I worked, I cut a half inch hole in the top for exhaust, and a hole that fit the size and height of the tail pipe on my Subaru on the front.

A mere 4-5 minutes of combusted unleaded, in the form of carbon-monoxide, was enough to send a baker's dozen of the black rice factories painlessly across the river Stix - all in one go.  My wife didn't approve of my mass killings and came to call the set-up "Mouschwitz" in order to highlight my evil ways.  But the house was soon critter free, and no more turds on the silverware.

I highly recommend this as a humane (albeit more disturbing) and time efficient alternative to beating, crushing, or shocking.