I really need help with raised veneer from moisture!

I bought this vintage chippendale mahogany partner's desk today at an outdoor market and before it was delivered it got damaged by the rain. The top is not too bad but the sides are "bumpy" where the veneer has been affected by the moisture. There are no splits or bubbles that I can see but rather a sort of all-over roughness. Can anyone give detailed advice on how to correct this without refinishing/sanding? I heard that you can re-wet it and weight it but I'm not quite sure how to go about it. Thank you!
q i really need help with raised veneer from moisture, painted furniture, woodworking projects
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