No real data on it either way. So far, the studies that have been done lack good controls and hard numbers to find anything out that would be statistically significant. That said,for some reason some doctors feel the need to warn about you ovarian cyst development when you start T, so basically just have to keep an eye on it if you are worried about your risk. "who the hell knows, probably not? but better safe than sorry, so get it all removed if you start to have issues,or when you have been on T awhile" seems to be the consensus of the medical establishment.
I should add the above is about ovarian/uterine cancer specifically - just realized your post was about cancer in general
also risks for everything medical will vary based on your health conditions....so talk to a doctor, etc etc