Well, for starters, begin with the definition of VOCs:
http://en.wikipedia.org/wiki/Volatile_organic_compound#DefinitionsThe Wikipedia article has a link to further definitions, but Canada apparently defines VOC within a certain temperature range, and their effect on global air quality -- their tendency to produce photoactive smog, I'd guess. In other words, Canada never promised, as the law was written, that you'd not get excess solvent in your room.
I'd suspect there are labs that would test a sample for you, but I'd suspect it would be expensive, and they likely work under contract. That is, they'd like to test dozens of samples, for a manufacturer, or government agency, not for someone who walks off the street. You could even call the manufacturer in person, they might be willing to tell you exactly what's in their preparation. Usually such things are trade secrets, but if they're not suspicious, there may be no harm in telling you the formulation, you're unlikely to replicate it, in sufficient volume, at low enough cost, to hurt their business.
I think you may be a little naive 'tho. You want to brush on a fluid mixture that will dry to a polymerized solid finish. That can only be done with an organic solvent. I suppose technically pure linseed oil does react with oxygen to dry to a polymerized solid. But there's no other chemical that does this. All paints and varnishes contain some volatile organic solvents.