Mark makes some good points. Howeva...
I believe I see what you're envisioning, a Super Man Shower Stall!
Showering in the stairwell, not on the main deck adjoining it. If that is the premise, not only will ablutions be performed in a phone booth-sized area, that narrow tread would be awkward to balance and maneuver upon, especially when shampoo froth is wanting to trickle into the eyes!
To continue with this conceit; I suppose a drain could be installed into the lowest tread for drainage, however a dam would be needed at the threshold to direct the rinseate into a holding tank, and not to simply cascade onto the ground just out from your entry way, like some Skoolie waterfall.
A permanent barrier at the threshold might likely create a tripping hazard, BTW.
You're getting into fairly low clearances there, so a low-profile temp tank that can be connected to the drain would fill the bill.
All stairwell seams would require caulking to prevent agua incursion, and a hydrophobic coating painted onto all surfaces that'll get wet, to facilitate cleaning & drying.
A series of belaying points on the ceiling to suspend a curtain from while in use and during drying would do the trick. In the event of staying in a populated area, a mirrored adhesive film on the door glass should afford privacy, unless said shower stall is internally illuminated!
I'm a heathen, so I prefer to shower al fresco. My site is situated and set up to afford no sight lines when showering with the garden hose. Tho I do tend to wait until past dusk and in the pre-dawn to complete comprehensive clean ups..!
Cold climates call for a different approach, natch.
