In my experience, those solvents behave well on wax phases. It should not be a problem for you.
It sounds like a good ol' "Vick's Vapo-Rub" matrix. My Mom used a ton of that stuff on us when we were kids. Can you slurry it up in water or does it just sit there? I would do that and try headspace SPME to determine it. I know that I can do menthol in cough drops by dissolving the drop(s) in a known amount of water and then do the menthol by headspace/SPME.
I took 526 mg of a cough drop and dissolved it in 20 mL of water. I then analyzed 1 mL of that solution by HS-SPME to get:
https://flic.kr/p/owVPpF
According to the label, it is 7 mg/dose. A typical dose is 3.8 g (mass of a drop). That's 1,842 µg/g or 48 µg/mL in my 20 mL of solution. That gives a massive response in my mass spectrometer and on one of my FID detectors. I would have to dilute it more for quantitative analysis. Perhaps this technique is too sensitive. 0.2% comes in at about 2,000 ppm in the petrolatum. The Signal-to-Noise on this "48 µg/mL" (if you take the dose as true) is 6,323:1 for the FID. On the ZB-5ms phase, the menthol peak fronts quite a bit. A wax is likely a better choice.
You might be able to do the menthol in the petrolatum directly using headspace analysis as the menthol likely won't partition into the headspace readily (it'll be pretty soluble in the matrix) but you might get enough for good quantitation.
I used:
SPME Fiber: Carboxen/PDMS/Divinylbenzene-2cm (Supelco, Inc.)
Preheat: 60 °C for 15 minutes in a dry-bath heater.
Extraction: Headspace (no stirring) at 60 °C for 30 minutes.
This is just a GC method that I have been using recently, it has no specific relevance to this analysis:
Column: Phenomenex ZB-5ms (30 m x 0.32 mm x 0.25 µm)
Injector: 240 °C, Helium carrier at 25 cm/s (methane at 40 °C), split ratio of 5:1
Oven: 40 °C for 2 min., 40-240 °C at 7.1 °C/min., 240 °C for 4.83 min.
Detector: FID at 240 °C, 30:300:25 H2:Air:He makeup gas