Hydrea is an oral chemotherapy medicine that is not likely to cause hair loss with the dosages needed to treat ET. You will want to take your meds with food and a full glass of water, wash your hands after handling the meds and up your normal intake of water throughout the day to help fush the toxins through your body. Most of us here on the site only have slight reactions to the meds. Mouth sores (drinking lots of water keeps this from happening) and slight headaches occasionally are the only ones I've had. As long as I stay well hydrated I don't have any side effects.
I'm 67, have ET JAK2, and have been taking hydrea for four years now.
My medical people tell me I'm more likely to have hair loss due to stress or aging, than from the hydrea.
Please rest easy and enjoy your trip.