Listen romex CANNOT be left into exposed areas where people live.

Cutting the drywall near the floor really isnt that bad. You can
patch and hack it up to your hearts content when you are
finished because you'll be covering it up with molding.

If your saving the effort (an money) of using an electician,
get new colonial moldings (4" high) and they will cover it
all up.

If you use condiut or BX cable in those areas, it'll look like crap.
If the time ever comes to sell it, it WILL be a problem with
an inspector. (they might not like it and may ask if you ever
got a permit for the work done)

Tom
P.S. the other option is if its a crawl space or a basement under the
floor is to drill up through the floor into the walls. Too much of a
pain
in the ass if you ask me.