Even humidification and drying under pressure is a good idea, but misting may be a little too random (even light misting) to insure an even application. Direct application of water to the back of the paper can result in new and more interesting problems than the cockling the piece is now experiencing.
If you insist on trying this yourself (as opposed to sending it to a conservator) you might want to consult with a conservator before proceeding.
There are potential pitfalls involving the kind of paper, the kind of pigments, the age and condition, etc. that should be taken into account before proceeding.
Depending on the value, you might want to check your coverage limits on your insurance. If the client is not happy with the results, you will more than likely be buying the art from them.
Another thought before I go...isn't there some liability on the part of the original framer to make corrections to something framed improperly? They are the ones that caused the problem (unless the client left the piece in the sauna a bit too long), and by working on the piece to make corrections, you assume a certain amount of their liability...well actually all of it since after you work on it there will be no evidence of where their work ended and yours started.