Hello from JustAnswer.
If only one tube is affected, then there would be no risk that both ovaries would be removed. If the fluid collection and infection is affecting only one tube, it is possible that it may also affect the ovary on that side and that the affected ovary may need to be removed. The likelihood that the ovary on that side would need to be removed is low, but there would be no risk that both ovaries would be affected and would need to be removed.
If I can provide any additional information, please let me know.
If one ovary is removed, there is no real increased risk of early menopause. Early menopause can occur, even with both ovaries intact, and the risk is not significantly different if one ovary is removed.
Whether there are other options for hydrosalpinx would depend upon what is found. If there is a small area of blockage, then surgery to open the blockage may be considered rather than removal of the tube. But if the tube is more extensively damaged, then surgical removal is the usual approach.
It is reasonable to proceed with surgical removal if the hysterosalpingogram shows that it needs to be removed. However, you can put a limit on what you are willing to consent to be done during surgery. For example, you can say that if there is more extensive involvement than is expected, that you would want to have further discussion before consenting to removal of both ovaries.