If your are doing headspace analysis, these organic acids are going to be tricky to deal with. They do not go into water well. And, if you put them in a volatile organic solvent and spike the solvent into the sample, the solvent can become the dominant vapor in the headspace and saturate the fiber.
You may be able to put the fatty acid into a solvent such as chloroform and add a few microliters of solvent to gram quantities of sample. But, you have to add sufficient quantities of the fatty acid to see it - and you must keep the solvent quantity to a minimum.
Another possibility is to take all of the tomato paste/ corn oil mix that will be used in your study and a portion of the fatty acid and blend them together. The problem of water soluability remains - and the acids may be only partly disolved. But, you need to be sure these acids are not subject to degredation.
And I will point out that these acids are not particularly volatile, so you may not find them transfering well to the fiber. I don't believe that I've noticed fatty acids of this size transferring significantly to a SPME fiber in the work that I have done. (but that may be a matter of how hot I've wanted to go with the sample or how long I've equilibrated the fiber in the headspace.) So you may want to try a couple of experiments to see if you can even see your internal standards. And that is as simle as adding a few flakes of each acid to a headspace vial with some corn oil and sampling it. I suspect the fatty acid may partition to the corn oil.
If you are looking for aldehydes and ketones as oxidation products, I would suggest that you look for an aldehyde or ketone as an internal standard. It is likely to be more volatile.