Its a bit unusual what you're doing. You didn't post your location, but are you sure there isn't an easier way?
A few years ago I was thinking of traveling to Bangkok for HRT as well. Luckily I didn't need to.
There's been posts here before about seeing doctors for HRT in Bangkok. I think its pretty difficult finding anyone since that's not how it works there. There was one place if I remember correctly, but I don't remember who it was.
You might also find a prescription from Bangkok doesn't help you with anything when ordering online to a different country. I don't know though.
There's usually a limit on how much you can take back with your. 3 months into Australia for example. I've traveled with HRT quite often and they have never even looked at it. Even if they did I doubt they would care unless they were after you for something else - assuming we're talking about estrogen, not testosterone.
I use implants these days, and I'm over a year between getting new ones. If you could find somewhere in Bangkok who would do them that could mean you only need to travel once a year, or less.