There is information on other threads about traveling with a hot pot but this is what I did:
The hack for this one,depending how long you will be traveling, is to keep all your old cups
At the end of every four weeks, sterilize and store the old one in a clean plastic bag with the date.

It is perfectly fine to use them a few more times- I never tested more than 4xs extra. Depending on length of travel and how many you can stockpile, you can either discard or rinse in soapy water, dry and bring home to sterilize later.

For longer trips, I managed to arrange some kitchen access every few days- friend, family etc. and sterilize a few cups in one session ( keeping parts of each separate)