I have a small suggestion; keep it in line with Faceless, and give it an effect based on the card it copies. For instance:
If the copied card cost is X, then Y.
X: bricks, Y: Attack: 10
X: gems, Y: Stock: +2
X: recruits, Y: Wall: +10
X: mixed, Y: Tower +5
which meshes even better with Far Sight (which can have trouble vs. gem decks), or
Gain N/4 random tower, wall, or resources, where N = copied card cost.
which is straightforward and hasn't quite been done, or perhaps even
Trigger non-summoning, non-Durable/Cursed, keyword effects of the copied card as though Shapeshifter had those keywords.
which if implemented would make the card quite good on Quick/Swift cards (and also be the only way to trigger Uncommon Flare Blitz but I'm not sure anyone cares).
It seems like Shapeshifter has the potential to do something more clever or interesting than just another keyword.
2019 edit: Shapeshifter is still quite bad.
I gave it another chance, because I had an ideal Far-sight, gems-unusing deck for it. I came to the conclusion that even if this were given Illusion keyword, or Quick, that wouldn't be enough to counteract how Barbz's Pupil is just as good most of the time, and when it isn't any other Illusion card except maybe
Eternal Dream would be better.
(Both Quick and something else would flip it into too strong, probably.)