I have traveled many places in USA, Canada, Europe, etc. with my machine and humidifier. It is usually easy enough to get distilled water just about everywhere. If there is none closeby, I have used tapwater without any problem. Air travel is already way too big a hassle to add the necessity of carrying water bottles which could leak out, and the bigget problem of dealing with bossy TSA inspectors. I have found that just getting my machine through the TSA is big enough problem, and they still go through that cutsey wipe and scan routine of the machine.
Just deprive TSA of that routine and get water at your destination, or for short term use tap water.