Thank you so much for all your helpful comments. It is clear from what other people say I'm not being a complete wimp about this, I'm not on my own!
With the helpful comments in mind, when I got my appointment letter, I rang the hospital to say that I wanted to have a general anaesthetic and couldn't contemplate the procedure without.
A couple of days later, a nurse from the department rang me, and arranged for me to have a scan, which I had a couple of days later. Then she rang me yesterday and said, after having looked at the scan, that everything looked fine, and there was nothing to suggest I would need the procedure and that the bleeding would probably stop if I reduced my HRT. (which I have, and it has).
She advised me to ring my GP if I had any other issues, but said for now, there was no cause for concern. She also said that if I did need the procedure in the future, there would be no problem having a general anaesthetic. So a massive result, and thank you all for your comments. I don't think I would have stood my ground without them.