how to de-select multiple faces?

I have a hollow plastic part with lots of faces created by ribbing and fillets inside and out.  I am trying to do a simulation by applying a pressure to all outer faces but am having a lot of trouble selecting faces in a remotely automated way.  Not all faces are tangent so I can't just use the tangency selection function.  When I drag mouse over the part it selects inner and outer faces which doesn't buy me anything.

Anyone have ideas on how to better do this?

SolidworksParts And Features