You could tried FT-IR. You should be able to distinguished cis and trans isomers using IR spectra.

FT-IR is not helpful, as the only difference is in the proton at axial vs equitorial position of cyclohexyl.

I have a different experience. There are some publications describing similar situation and IR was used a a method of their choice. E.g. http://journals.tubitak.gov.tr/chem/issues/kim-02-26-1/kim-26-1-12-0010-14.pdf

But you can of course try a different approach.

You could try to determine them by GC(MS) after derivatisation with an appropriate agent, for example BSTFA. Alternatively, they could be separted using HPLC...

I'd look at GC, either directly or after derivatisation. A shape-selective stationary phase (eg a cyclodextrin-based chiral phase) might be useful.

I agree with Thomas Schettgen, though I would expect also RP-HPLC could do a good job. However GC is easier to handle.

Anyway by such means you would only be able to separate, but not to identify. Mass pectrometry as a detector will not be of much help. GC-IR might help, but there is not a lot instruments areound that operate properly. I guess at some poit you need to do preparative separation and NMR. There prep HPLC is somewhat easier to manage than prep GC