Before going further, ask your self this:
You need to drive your UK-purchased car in the US now. OMG, US is right-hand drive but the UK is left-hand. you now need to change the position of my gear and streering wheels to the other side.
Does this sound logical to you? Does it make your life comfortable? Are you gonna buy a new car now?
Same logic my friend. As @DanielRHicks and hillsons said, brakes are not needed to change.
I would rather focus on using the road sides correctly as US is for right-hand drive. Unless there is any law about changing the shifter positions, don't do it. Just ride as you would ride, but try to get the road side correct.