FOR THOSE WHO ARE ALSO CURIOUS ABOUT THIS:
The answer is YES
, it is possible to just swap the mirrors. My BMW service advisor told me I needed a retro-fit cable for the wire harness and that I would likely need to have the car programmed as well, (which would cost about $120 for 1 hour of programming + $65 for this cable).
However, none of this is true. I simply swapped the mirrors and I programmed my garage doors to it. Thats it! No programming or wiring was needed