Honestly, don’t worry about picking one to identify it, the mushroom portion of the fungi is the equivalent of the the flower on a tree.

If you’re really so concerned, place the cap face down after picking so the spores still end up on the ground.

Or if you really don’t want to damage one, use a dentists mirror, or a telescopic inspection mirror, or even a compact mirror, and place a piece of paper with a small hole cut in the centre and a cut from the outer edge to the hole around the mushroom (think of the collars they use at the hair dressers) use a small piece of masking tape to join it and camping peg to pin it to the ground, then return to it later for some spores to inspect and