Alterations to the paper both before and after the print job could have negative effects. I suggest doing a test batch first so you don't ruin your entire supply. Thee option I find most likely to work is clear spray paint, but you would only want to apply this to the finished prints as sending something spray painted through your printer could gum up your machine. (Also, printer ink may not even dry properly without smearing on any shiny surface not designed for printing.)
AFTER the print job, I suggest letting your printed sheets fully dry before trying to apply the clear spray paint. If your ink is not fully dry first, the paint could cause the ink to bleed. When you spray the paint, be careful not to apply it too thickly or unevenly because thicker, wetter areas will likely make the corners of your paper curl.
I do have one alternative suggestion, but it's more labor intensive. Thick paper can be dipped in clear melted wax to create a somewhat shiny surface finish. (I've seen this done with color photo prints with no detriment to the inked image for an art installation one of my peers created).