As long as the cervix and ovaries will remain, hormone production will continue normally, and sexual stimulation should remain normal, and the immediate and long-term effects of just removing the uterus should be rather minimal.
Will anything be done about the cyst you have on one ovary?
If having that type of partial hysterectomy, removal of the uterus, will alleviate your pain, and will eliminate your problems with constipation and painful bowel movements, what is your concern about having it done? Why do you need our recommendations?
My only suggestion to you would be to consult a gastroenterologist to see if they could offer any way of possibly reducing your bowel movement pain and discomfort until you can have the partial hysterectomy done. Also, I would solicit their opinion as to whether the surgical procedure would definitely correct the problems you are having, and their opinion of why you sometimes see blood when you wipe yourself and what, if anything, could be done about that now.