I am very close to a woman who has needed a hysteroscopy, and learned a lot about that procedure from her, Some of what I learned might be helpful, so I decided to post on your thread even though I am a man. Before undergoing the procedure, the aforementioned woman informed herself thoroughly about it, and she then explained her me in some detail.
What she was told is that although some women tolerate it very well, apparently that particular procedure is, on average, rated as being the single most painful GYN procedure that can be done on an outpatient basis. The majority of women tolerate it but a significant minority need to ask for it to be stopped midway through due to the discomfort, and it is therefore 100% reasonable for any woman to say they want it done under GA. The main disadvantages of GA are that you might need to wait longer to have it done, and if there is a polypectomy happening during the hysteroscopy then there is also some increase in the risk of uterine perforation, although that risk still remains very low.
Despite the disadvantages, I would hope you can just tell the nurse that you would not be able to tolerate this under local and need this to be done under GA. If the nurse then persists in any way, for instance by asking you to "try" / by claiming they can stop the procedure at any point, you might then consider telling her (hopefully it will be a female nurse!) something like "you are making me very uncomfortable, I need this done under GA for personal reasons, and I do not wish to discuss it any further". If the nurse is not a complete idiot, she should then hopefully close the discussion without demanding further details.
Please accept my apologies for posting here despite being a man. I am trying to be helpful. If you find this unhelpful and want my post withdrawn, just let me know and I will report myself to Mumsnet, or you can report it for me.