A simple keybind mod to select a random character.

How to use
Bind it to any key you want in Options > Mod Keybinds > Random Character
Then press that key to select a random character.

I've disabled its ability to change character in Lobby for now since it might caused some bugs so now it only works in the main menu. I may update with ability to change character in Lobby later once I could make sure that it wouldn't cause and problem.
It seems to be impossible for me after all. After I've read the network code, it seems that host only request preferred character data when player joined so changing preferred character after that doesn't have any effect to the game.
Some others may have a way to deal with this, or I may read the code wrong but for me, I'm unable to do it. Sorry for getting your hopes up.