On this side of the Great Pond we would try and do some detective work
from the inside. I wouldn't want to comprise the integrity of the
exterior.

Is the wall drafty? Do you feel breezes on cold days coming from
electrical outlets, from behind moldings, from around windows?

Can you remove any electrical outlets on that wall to see behind the
box? Are there any closets, cabinets or furniture on this wall that
you can drill a hole behind to see if there is anything in the cavity.
You'll have to patch those holes but at least your working in a
concealed area. Is there an attic that you can get into to drill a
hole down thru the top plate into the cavity? Again you'll have to
patch but it will provide a concealed way to view the inside of the
cavity.

Do any neighbors have similar homes, built by the same builder at the
same time? Do they know if they have insulation in their walls? Are
their walls as colder, warmer or the same as yours?