Good point---the USA has a limit ($10,000) on how much you can carry out. If you take more than that, there are documents you must file. When I visit in Europe there is a $10,000 limit on what you can bring in without a similar paperwork drill.

This is why I suggested having a bank account overseas, so you can wire money into it and have it there when you arrive; also, safer than carrying. I think most countries in Europe will allow non-citizens with a valid passport to open bank accounts, and these accounts can be denominated in dollars, but I am not familiar with the rules in every country. At one time, Swiss Banks were allowing accounts to be opened and funded by mail from the USA, (you did not need to be there personally) but I don't know if this is still possible.

But in a bug out situation, I would do the paperwork and try to take the cash if nothing else were available. Otherwise, I would never get access to the funds at all.