Can I use paper shield on a shadow event card? Does the 2 gold it costs to put an event in the shadows count as a gold cost?

Yes, you can use Paper Shield on appropriate Shadow events.

The 2 gold to put it into Shadows and anything you have to pay to bring the card out of Shadows are not considered part of the cost of the event effect. They are costs of the Shadow mechanic. Paper Shield can be used on any Shadow even effect that does not have a prohibiting cost as part of the card's triggered text.