You should be able to do this with an odd & even Page Layout, available through File/Page set-up, if I recall properly. Just set up the odd and even footers as you like, and they will propagate automatically.

Just be careful to use section breaks with care, if you insert a landscape or other sized page. Word needs both sides of the virtual page to be the same, just as if it were a physical page. Otherwise, it will try to continuously re-paginate.

Best,
Ulodesk