EgnirysFaye has it right. I previously identified as transsexual, so I've done a fair amount of research on binding... Binding properly won't cause any actual harm. Binding for a very long time (like all day every day for several years) will cause some break down in the tissue, causing some sagginess. But that's really all there is. It won't cause cancer, and binding a few times a year isn't going to do any harm at all.
So enjoy your crossplaying!