Maybe some players don't know, but when the vote menu screen appears, there is a "Config" tab. In this, you can setup a hotkey to prompt the vote menu dialog.
You can also go to the "user.ini" file located in your system folder of unreal tournement, and set it up by hand. I have it on the "F8" key, so it looks like this:
F8=mutate bdbmapvote votemenu