Unplugging your controller is furthermore not a solution because frankly, it's a very unhealthy attitude to consider it your customer's job to do tasks that should be unnecessary to use your entertainment product. And in fact, if adding an option for this were too much work or too difficult, a notion I find positively ludicrous, then given the lack of controller support it is an utter and complete no-brainer to default it to off.
I speculate that it's some manner of library used that provides the controller shake as part of a "your character got hit" package of functions, and that it was possibly not actively coded IN as a feature, merely not caught because as controller was not within dev scope, so controllers were not present in testing environments, possibly? But regardless... this needs sorting out.
Giving us the launch option is an inferior option as well... I'm a steam user and when I launch the game, it launches the launcher, which in turn launches the game after discarding any launch options given, which I would then have to mess about with much more to launch the game directly, costing TW the option to show us germaine stuff about the game in the launcher. Maybe add an option IN the launcher to launch the game without controller, if it can't be done within the game? But the thing is, it is ABSOLUTELY possible to do this within the game. If you have access to the software but you cannot alter when the rumble activates, then it would either never rumble or always rumble. The game is already selectively activating the rumble. Somewhere in the code is a function that fires when your character is hit. Start there, trace function calls, sooner or later you will find something that activates the rumble. Comment out that, or put in a conditional based on if the option is turned on. Done.
I repeat, this is an absolutely dire oversight that's unworthy of you having it in your otherwise impressive product.