When an opponent failed his reflex save and the weapon got stuck in the Resinous Skin, is the following try to pull it free another action than a free action? What kind of action is it?
Resinous Skin only says it takes "a successful Strength check" and there's no default action for an ability check.
Personally I would make it a move action, similar to that used to Manipulate an Item.
YMMV, AKA "Expect table variation."
I'd rule it as a standard action, the same as removing a weapon stuck to a creature with adhesion. But I could probably easily be swayed into making it a move action as Grick suggests.