I'm at work (duh..) so I can't test this right now, but could it be that simply?
Unless you're firing off any Virtual Combat mappings with something other than Combat Hotkeys, you can just disable the Combat Hotkeys key map. Some people like to add Combat Hotkeys to the default toggle. If you do that, then it doesn't sound like you'll really need a new button, you just need to turn off key maps and broadcasting mode