How can I examine fruits or vegetables in a market, while minimizing mechanical damage?
The first step is to only pick up items you're likely to buy. Then you should only have to put down items that have an actual problem already.

For some things you want to check for ripeness, but under-ripe items are more robust, so it should be possible to pick them up gently without damage and put them down again. After all, it's handled by people and machines quite a lot before you ever see it. If on the other hand you're looking for something underripe so it keeps for longer (and you can't go by colour as with bananas) you will need to be very gentle indeed handling potentially ripe items.