What wall color to 'blend' different wood tones?

I am a realtor who is about to get a listing that needs staging.  The one thing that hit me about the home is there are too many different woods visible in this open plan layout: kitchen cabinets, hardwood floors, laminate floor, two table/chair sets, living room furniture and wood trim.  All walls are white.

Some of the woods, like the tables, I can cover.  I found a great piece of decorator fabric at a resale shop that beautifully combines cool and warm browns and blues, greys, & greens.  I'm thinking of painting the wall that combines the dining area and kitchen a pale blue-grey.  What do you think of this color to hold the woods together?

 I hope to use the fabric as a table cloth for the dining table, a window treatment for the dining area, valances for kitchen and dining windows + seat covers or table runner for dining table.  It's about 4 yards of fabric (got it for $150!).