GC/MS can detect some of the pyrolysis products.
Don't know how you plan to pyrolyze the paper. One way is to heat in a test tube and analyze the liquid that comes off. Often, this is done by dissolving the pyrolysate in a solvent and injecting the solvent (after filtration) into a GC or GC/MS.
There is a different route that might be easier. There is an pyrolyzer accesory for GC. You put a small amount of sample (usually in the milligram range) into the pyrolyzer. The pyrolyzer takes the sample through a thermal temperature program that takes the pyrolysis gases directly to the GC or GC/MS. One problem is that the pyrolyzer accessory is relatively hard to find.
A note about pyrolysis analysis. The samples tend to be dirty. It is usually better to try them on a GC before trying them on a GC/MS. Work out the analysis details on the GC first. If you try pyrolysis directly on the GC/MS, you could damage the instrument (well, at least require instrument cleaning). This won't make the college or university happy.