I don't think I'd go 4 days without wearing them. If I go 2 hours without wearing them, it hurts to put them back in. I would think you'd have to start over or possibly get new aligners depending on how your teeth have shifted.
Whenever I know I'm not going to be near water, I take a bottle of water with me. You can also buy travel toothbrushes that already have the toothpaste on them. I bring one of the invisaligner cases that my
ortho gave me and I'll just stick in it my pocket or backpack. I've done this for times when we're in parks for long periods of time. We also tailgate for college football and making sure I have a bottle of water, my travel
toothbrush and case works out just fine for me.
Personally, I've spent a lot of $$$ that could have gone to good use in other places. No way would I risk my teeth shifting b/c of travel. Maybe you should talk to your ortho about more traditional braces? That might be a better fit for you.