I would give that a big ol' no, I'm afraid.
They really aren't a 'petting' kind of critter. As folks have mentioned above, they have delicate skin which is also very porous and they will absorb and be harmed by all manner of chemicals.
Their limbs and muscles are designed to work in the buoyancy of water, and they cannot safely move outside of it, trying to move outside of water could really hurt them.
They are also easily startled and VERY wriggly, and you should avoid holding or handling them at all costs- much as we'd all love to huggle them for being so adorable.
When I clean out my tanks, the braver of them will come and try to eat my elbow, so on tank cleaning days I wash my arms thoroughly, dry them off, don't use any hand creams or body lotions etc, and rinse them in the first bucket of tank water I take out before I start moving decorations etc. I recommend keeping clean tubs to hand to gently scoop them into along with some water if you ever need to transfer them or isolate them. Never, EVER try and carry them even a short distance, they're too precious!