You'd have to create some new team skins, that don't look like team skins, I suppose. Take some generic skins and save them as the names of the team skins and run that as a mod. Of course you'd only see it on your end, everybody else would just see the normal team skins. The "team overlay" is just a little part of the hud in the upper right hand corner that shows the names and health of the players (and also their location and current weapon if it's Siege) in team games.
The "team beacon" is that little Imperial/Rebel symbol that appears over the heads of your teammates. ONLY your teammates will have a symbol floating over their heads (unless you're in spectator mode in which case everyone will have it). Turn it off and everyone just runs around without anything floating over their head (except the odd chat box).