MORPH: HANK PYM: Give Giant-Man a move or close combat action that deals no pushing damage. After the action resolves, replace him with any character with this trait on the same click number.

On a number of clicks Giant-Man's got Charge, and since Morph can be a close combat action you can tuck it into Charge. If Giant-Man's already got a token and uses Charge & Morph, would he take pushing damage?

It can be given as a part of Charge.

He will still take pushing damage, because it was the power action for Charge that caused it, not the free close combat action within it.