Do I HAVE to spend a shield to reload, or if I have it on say, a K-wing, can I use the reload action?

Short answer: Yes, you can "Reload" your Bomblets.

Unlike mines such as Proximity Mine or Connor Net, there is nothing to prevent the Reload action from restoring a charge to Bomblet Generator. This benefit of this card, however, is that you can restore both of the card's charges for the cost of a single shield, instead of spending your action to Reload, and being unable to attack that round (thanks to your newly-acquired disarm token).