I would assume that your outside shower is located at the rearish of the trailer underneath the bed then.
Here are some photos of how the plywood is laid out under the bed and what you would have to remove to access the area.
The panel marked C is easily removed to give access to the front half and none of the wood is glued. If your taps are in this area you are in luck.
Panel D that goes across the whole rear width of the trailer is another story...
It is part of the entire bed structure as the beams do not run from the front all the way to the rear. Start taking screws out of that panel and the whole bed will collapse.
Here are some photos of how the plywood is laid out under the bed and what you would have to remove to access the area.
The panel marked C is easily removed to give access to the front half and none of the wood is glued. If your taps are in this area you are in luck.
Panel D that goes across the whole rear width of the trailer is another story...

It is part of the entire bed structure as the beams do not run from the front all the way to the rear. Start taking screws out of that panel and the whole bed will collapse.