Never heard of isotopomer, had to look t up. Normally you would use an istope ratio GSMS (GC-IRMS) to measure isotope ratios. After converting the compound to CO2 you'd measure mass 44/45/46. With the conversion to CO2 you'd lose all the isotopomer information you are looking for so that is not an option.
So you have to use a "normal" GCMS but these are not very good in measuring small isotopic differences. It also grealy depends on the fragmentation of your compound, you have to look at the isotope pattern of every fragment and hope that are enough unique fragments to make out the isotopomer. Maybe you can see differences if the abundance and enrichment of the fragments are high enough, maybe if you are very lucky you could recognize..........
If it does work it won't be easy to interpret the results. If you Google you can find articles where they are using GCMS (in combination with NMR) to do isotopomer analysis.
Sometimes restrictions that are imposed, like in this case "not from NMR", is just not a real option. As far as my knowledge about NMR goes, NMR is the best option.