Private lobby and private server is not exactly the same thing. On a private server, is sv_cheats 1 is on anyone can take advantage of that, but you can't enable the sv_cheats from client side.
On the other hand I would like to point out if you roll with private lobbies, who ever is hosting that lobby is going to have a monstrous ping/game feel advantage.
Thanks for your feedback @Eon
Think the private server would work better then. I am sure @stroes won't mind adding the commands for us before each game commence.
The only other problem is we will only have one server, so one match at a time.