It's going to be compromised, of course, and there will be issues, but looking at how other canard Deltas fare on carriers, perhaps a much bigger wing is unnecessary -- the Gripen boys have done some interesting sim work, Rafale manages well, and though the MiG-29M has more wing area, it's all added at the tips, the flaps, and via a new leading edge.....
The question isn't whether it will be easy, the question is whether it's a possible back up/alternative.