I don't see anything stopping you from holding a weapon in your hand but not wielding it. Certainly, that applies to light shields and bucklers. Although a force shield can be wielded "as if it were a heavy shield," you can also choose not to wield it. It is weightless and encumbrance free. Further, aside from the fact that you can only not hold something in the same hand because "it is so heavy," the ring of force shield says nothing about imposing the penalties of a shield. As a matter of fact, is has no armor check penalty, and thus, I think we can safely conclude it has only the characteristics described in its entry.
Since it is not actually a large shield, I don't imagine you could bash with it. Bashing is something described under the item "large shield," which it is not.
The only thing you can't do is simultaneously wield the force shield and wield the weapon. The weapon does not preclude wearing a ring, and donning the ring does not require you to wield the shield or even activate it.
"Wielded as if it were a large shield" seems to mean "receive a +2 shield bonus to AC, but only if wielded." Because wielding a shield precludes wielding something else, you can't use the weapon.