Use "x360ce" (Xbox 360 Controller Emulator). Drop the 64-bit version into your NHL 09 folder. Configure the triggers as analog axes, not buttons. Save the xinput1_3.dll and overwrite the default.
So, you’re ready to experience this classic for yourself. Since EA no longer sells the game, finding a safe and complete version requires some detective work. The best sources are often digital archives and dedicated fan forums that preserve classic games. Here are a few examples of the types of places where you might find what you’re looking for, always remembering to verify the file's safety: