Safe to use water for handwashing, if you literally are flushing the lines at that time?

OK, so we're planning to go camping end of the month but we're going to have a problem getting the camper prepped.  Our tow vehicle is going back to the shop for a possible compression issue, so we might end up going to the campsite with RV anti-freeze in the lines.

Right now I'm debating between either taking a 5gal water jug to the camper and using the pump to pull it in and mostly flush the lines, or (if we don't get the truck back before our trip) filling the tank at the campground and flushing the lines at our campsite.

If we do the latter, obviously we'd not be using the water system for anything besides the toilet, but would said water at least be safe to use for hand-washing?  As long as we're running clear, it should be, yes?