It's not too much risk removing the tent. It might change shape and shrink a little when you wash it but it's no worse than when they were new (which is a PITA). You used to be able to get factory replacement tents when WilderNest was still around but that's been years since they went under. Take the opportunity to replace all the screws with stainless ones, get a box from McMaster.
As far as washing them you do have to be careful. As NorthernWoodman mentioned the tent is urethane coated nylon, so there are not a whole lot of chemicals that are safe for both. Regular mild dish soap is fine (this is what I use). I have a couple of bottles of stuff called Sail Bath that works, too. It was made by Davis for cleaning sailboat sails. It does not seem to harm either the urethane or nylon but as far as I can tell it's no longer made.
Do what climbers do when we clean ropes, wash it in the bath tub. When you dry it hang it carefully so it's not drooping, that's what distorts the shape mostly. Lay it out, use lots of support or just put it back on damp and let it shrink to the frame. You don't want the fabric laying on top of itself wet and there's not much better way than to let it dry on the camper. Pick a weekend with good weather and just leave it open for a couple of days to dry.
The main reason why WilderNest tents fail is the urethane coating separates from the nylon. There's not much you can do to avoid it forever but being gentle will keep it sound for a long time. Problem with mold is it gets into the nylon and forces the urethane to peel away, so if you can stop it right away that's best. Open the camper periodically to keep it dry, definitely open and dry after using, etc.
I would avoid trying Nikwax on the nylon unless the urethane coating is already gone. The fabric itself was waterproof from the factory and all it needed was the seams sealed. Most people mistake condensation inside for a leaky tent, not many of them actually leaked but they did not breath either. Now there's more and more of them that are actually leaking as they get old, though. Anyway, putting something like Nikwax on it might cause the urethane to come off, so I'm one to avoid using anything that soaks into the nylon. I also clean the tent of pine tar and bird poop for the same reason, to keep them from acting as a solvent on the urethane.
One thing to realize is that you might never get mold and mildew stains off the fabric and so don't try. Wash the tent, dry it, seal it and spray Lysol on the outside (Lysol is the best way I've found to stop mildew) and then just use it. Using it is actually the best way to clean the stains, UV bleaches the fabric over time. The tents when new are very green and after a few years they fade to a very pale greenish.
