Does 2mm make a difference?

Got myself 2 sets of brakes - Avid Elixir R with 185/160mm rotors and a set of Hope Tech M4 with 183/160mm rotors.

I'm not that bothered about the rotors but was wondering what I should be aware of by running the Hope calipers with the Avid rotors? Got a new bike and the Avid brakes stop me but I don't like the feel, so was thinking of putting the Hopes from previous bike on it...but I'm clearly a lazy barsteward and can't be bothered changing the rotors!

So, will 2mm difference affect the front brake? The braking surface on the Avid rotor appears to be about 2mm greater than the Hope rotor as well, that isn't a problem as at least I'd know that the pad was making full contact...just wanting to know if the 2mm difference will affect the brake i.e. prevent the wheel turning or catching, etc.

Happy to stick a washer on the mount to move it out slightly, but what size washer would I need? I'm guessing a 1mm thick spacer/washer?

Thanks.