At those concentrations, a simple solvent extraction of the paper followed by a direct injection into your GC should do the trick. When analyzing short-chained carboxylic acids, you probably want to use a wax column of some sort.
Go to restek.com, choose the "resources hub". Search the chromatograms for butyric acid and you will find app notes that show their Stabilwax DA could be what you want. Agilent.com is a good place to find columns and application notes as well.
Water extractions might not be what you want as the thermal expansion of water is enormous and injection of 1 µL in standard split/splitless inlets will overfill it. Precision problems are likely to abound. Other solvents like methylene chloride or even methanol are better from a thermal expansion perspective. Methylene chloride has it's problems from an environmental perspective.
You have a bit of an advantage from that standpoint in that with those types of concentrations, you can likely run at a pretty high split ratio. You're not trying to find a needle in a haystack.
It's tough to "get somethin' for nothin'" in this game. Good luck.
BTW, yesterday I took some cardboard from some secondary packaging I had here in the lab. I cut some 4 cm2 pieces and placed them in 2 separate 21 mL headspace vials. I had previously determined that it took 150 mg of MeOH to saturate the 4 cm2 piece of cardboard. To one vial I added 200 µL of MeOH, sealed vial. To another I added 200 µL of MeOH:BF3 reagent (Sigma-Aldrich), sealed the vial. I heated those in an oven at 60 °C for 1 hour then cooled them to RT. I opened the vials and added 5 mL of water then resealed them. Then I analyzed the water/cardboard mixtures by headspace GCMS (solid-phase microextraction sampling). Compared to the blank prepared using MeOH:BF3 and water (200 µL reagent, no cardboard) there was a "bunch-o-fatty-acid-methyl-esters" in there. Not so much butyric acid but C6 and heavier for sure.
