I've seen little 12v water pumps with sprayers, with a bit of hose or tubing to draw out of any pail or pot. Heat water on stove, combine with room temp water in a pail to get proper temperature.
You sure can set up a shower in your TC. That pan doesn't have a tall enough lip to hold the curtain in place, though. Nor to contain splashes if you feet slosh the water too much. Walmart or Lowe's or any places like that sell totes (Rubbermaid, etc) that come up higher. I've heard that hula hoop trick before; if you have a way to hang it from the ceiling you are in business.
