Depending on the item, I have (in the past) been advised to either leave it alone, or rewet it - and dry it flat, or in extremes patch it very carefully. I was also advised to find a ehem... antique dealer, since many times antique dealers 'fix' antique furniture before selling it.
I mean no disrespect or censor in that statement. Disclaimer: it is um, poor business practice to repair or replace antique veneer and then sell the piece as 'original'. But, realistically, it is done quite a bit by either the original owner or by someone else. nuff said.
Fact is, the antique dealers in your area may be able to 'refer' you to someone who knows how to er... 'fix' it. And you can get some pointers from them.
I've done something similar to a arts & crafts sideboard that has been in my family for 3 generations. I'm not selling it... and yes... <smile> it now looks pretty dang nice...
Of course, if your piece is not an antique and if it's not particle board underneath the veneer and if it's really veneer and not some cheap laminate plastic garbage... then get the sander. Go carefully...