I'm a newbee, but that's never stopped me from posting stuff in forums.
Hope this works for some.
Below is a pic of a no-mess device to clear slow running bath-sink drains. It goes down below the overflow cutout in the drain, so that the push is put where it will do some good.
Made it out of a bulb from an old turkey baster and a piece of plastic pipe with a few wraps of duct tape to better seal it in the drain pipe.
Used it on 3 drains. It works.
For a shower drain trap with no cutout, I found that a plastic bottle about the size of the drain opening, works slick. No need to use a plunger, just push the bottle down and the clog is gone. Of course, don't jam it down as that could mess up the trap joint fasteners.