Happy Father's Day!

We picked up a couple of pieces of bedroom furniture from Grandma's basement to
use a starter furniture for my daughter's apartment. The best I can estimate
from the label on the back is that the pieces are at least 82 years old. (The
Conewango Furniture Company apparently went out of business in 1934.)

SWMBO wanted to clean them up, so she grabbed a bottle of Murphy Oil Soap and
went at it. The results can be seen on the rag in the image below. The "dirt"
seems to be more brown that the grey I would expect if it was just years of
dust. The pieces were not caked in grime or anything like that, in fact they
seemed pretty clean.

http://i.imgur.com/9CgQu64.jpg

Murphy Oil Soap does say that it will remove "wax buildup" but I don't know
if the brown on the rags is old wax or actual finish. The finish was not shiny
before the cleaning and doesn't look much different now.

OK, so the main question is this: What can I (easily) apply in the next day
or so to enhance/protect the finish, keeping in mind that they will be loaded
into my trailer for the move on Wednesday. Unfortunately, I do not have time
to do a multi-step, hand-rub restoration. We are not looking to turn these
pieces into showroom pieces, just shine them up a bit for my daughter.

How much of a disservice would I be doing if I used one of the over-the-counter
"polishes", such as Old English, Pledge, etc.?