My darkroom, which I've been using for the last six years, also has no running water.
I make the exposure, process the paper until fixed and then place it in a holding tray. Once I have a couple of prints in the holding tray I take them through to the (non-dark) bathroom, hypo clear them and then place them in a second holding tray in which they stay until I'm ready to finish up. Then I complete their washing and put them to dry.
With frequent changes of water in the first holding tray, it's a system that works well for me.
All the best,
Frank