If this doesn't get me beat up it may make some think I'm weird, but here's what I do to my sink drain once a year (plus the one time I actually needed to). Take the nozzel of the garden hose, shove it in the drain hole, wrap a towel around it to keep the spray from getting you wet and squeeze the handle. If the boat is in the water you might make sure nobody is on the dock next to the thru hull drain.
Your shower drain might be a different story if, from what I gather in another thread, it goes to a sump with a pump. Maybe don't squeeze the nozzel so hard??