The reactive nature of the hydroxyl radical is going to cause you many problems when it comes to getting it through the GC column. I don't see that you'll have success with the direct approach you're suggesting.
If it were me, I'd find a way to trap the hydroxyl radicals. Make them react with something else that will give you something you can determine by GC.
Years ago we evaluated a technology that was supposedly generating free hydroxyl radicals, blowing them around the room, and killing microorganisms on the surfaces in the room - by merely circulating the air in the room. We didn't find it to be incredibly efficacious in its intent BUT as part of our testing, I created a gas standard of toluene in nitrogen. We fed it my gas standard and then collected a gas sample coming out of it. Sure enough, when you were standing in the outlet stream of the device, you could smell the "barn yard" coming out. Hydroxyl radicals react with toluene to make cresols (meta and para isomers, also very stable). So, the device was generating free hydroxyl radicals but we didn't find much evidence for disinfection of the room. As I recall, the yield was not great but the residence time in the device wasn't long.
O2 and N2 are not difficult but you need a specialized column (molecular sieve) and I'd recommend a pulsed-discharge helium ionization detector to see them. A thermal conductivity detector will also work for this as long as the required limit of detection is not too small. Mass spec is tough because you almost always have as little bit of O2 and N2 showing up in your tune. It's difficult to get an absolutely perfect seal.
I did find a reference for determination of ozone by GC:
https://pubs.acs.org/doi/abs/10.1021/ac ... ode=anchamH2O2 presents the same problems as hydroxyl radicals. I'm not optimistic about that one either.
My $0.02, is that something like what I describe here will likely be your best bet. To do this right, I fear that it's not an easy undertaking.