Hello Clover! I've done this before and got away with it, so it may be worth a try;
Dampen the paper from the back (face down on hard flat but clean surface) but don't soak it and try not to move it around, let the water dampen the paper by leaving it for a few minutes, then, still face down, find either a piece of glass, or stiff flat clean plastic and lay this on the back of the paper, suitably weighted evenly and leave for a couple of hours or so.
When you remove the weights and the stiff backing you should have lost some or all of the cockling.
As I've said, this has worked for me, but if you had thought about binning your painting, then you nothing to lose.
Lets know if it works for you.
RSC Wigan / Warrington area