Which file sets the default console key?

BaseInput in the game's Engine\Config folder, under Steam\Steamapps\Common\Killingfloor2, with the line ConsoleKey=Tilde.

How do I disable the tilde console key entirely?

Delete the Tilde value from the ConsoleKey line.

Binds & Console

KF2: Change or Disable the Tilde Console Key in BaseInput

If the tilde key keeps opening the console while you type in chat or use a keyboard layout where it is awkward, you can change it in the game files. This short community guide shows how. A second method that edits the user config instead is in Enable the in-game console.

Steps

Go to the folder where the game is installed, then Steam\Steamapps\Common\Killingfloor2\Engine\Config. The author's copy is on drive G; by default it is on drive C.
Find and open the file named BaseInput.
Press Ctrl + F and search for ConsoleKey=Tilde.
Change the value to the key you want, or delete the Tilde option to disable the key completely. For example, to open the console with the M key, set ConsoleKey=M.
Save and enjoy.

Note that updates or file verification in Steam can restore the original file, so repeat the edit if the key reverts.

FAQ

Which file sets the default console key?: BaseInput in the game's Engine\Config folder, under Steam\Steamapps\Common\Killingfloor2, with the line ConsoleKey=Tilde.
How do I disable the tilde console key entirely?: Delete the Tilde value from the ConsoleKey line.
How do I bind the console to the M key?: Set ConsoleKey=M.