You are basically being asked to provide a devil's proof (Prove that devil does not exists, its an evidence pattern : https://en.wikipedia.org/wiki/Probatio_diabolica ).
You are being asked to give a divorce documentation FROM ALL COUNTRIES INCLUDING SK.
But since you are saying that she never married in the first place, it means now you have to prove that she never married ANYWHERE and TO ANYONE.
Proving negatives like that is HARD.
What you need to do is to find a proof that she never married in SK and that her legal marriages in SK does not exist. That should be a starting point. Beyond that, only a good lawyer can provide help.
Interestingly, IRCC has not opened their own cards, so you don't know what they have on her. Proving what they have on her incorrect may be easier. But, I doubt IRCC will provide that evidence for examination unless challenged in a court of law. I may be wrong, others like @k.h.p. and @scylla may know more.
If you are denied your application, assuming yours is a genuine case, I think it will be denying fairness by the burden of legal cost.
Not everywhere. If they can prove they weren't married in the places where they have lived that is fine. It's not all about proving that you've hadn't had a wedding it's more about not having declared being married versus single in any document for the period they were together.