Mice are classed as vermin for a reason. (Disney has a lot to answer to).
Mice spread diseases such as hantavirus, salmonella, and lymphocytic choriomeningitis (LCMV) through their waste, even if you are careful not to touch them. Mouse faeces and urine can dry and turn to dust, spreading viruses through the air we breathe. Every time to go into your shed you will be inhaling this stuff. One mouse can soon become 10/20/30.
You can buy Mouse repellant spray that you can spray in your shed and over your garden tools. Fill all holes into the shed with an expanding foam filler.
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If all that fails then kill the little baskets :-)