Wait - I'm confused... You say "set it to 1 for products the shipping should apply to"... Do you mean the Free shipping discount? So I would put a 1 for the products that I want to DISCOUNT the shipping cost. Correct?
And the cart column - that should be different name than the db column, correct? or should they be the same.
Does it matter the "type" of the cart column? (number?) or text.
Thank you.

Create a db column for shippable.
set it to 1 for products the shipping should apply to and 0 for products it should not apply to
create a cart column for shippable
bind the cart column and the DB column in the add to cart button.
it will get a little different here though,
In the eCart object, create a new calculation called shipWeight set the calculation to:
(([shippable] == '1')?[Weight]:0) * [Quantity]
Then on the confirm page for power store, find the followng code:
$Shipping_PackageArray[$Shipping_PackageIndex]["PackageWeight"] = "".WA_eCart_FormatNumber($WA_Store_Cart->TotalColumn('TotalWeight'), true, 1) ."";
and change it to:
$Shipping_PackageArray[$Shipping_PackageIndex]["PackageWeight"] = "".WA_eCart_FormatNumber($WA_Store_Cart->TotalColumn('shipWeight'), true, 1) ."";
