How can a woman seek divorce from her husband residing in another country, given the absence of documents proving the marriage, if the husband refuses to divorce her and threatens to leave her in limbo?

Divorce occurs either by the husband initiating it or by the ruling of a Muslim judge. If your husband refuses to divorce you and you are harmed by remaining with him, then refer the matter to the Sharia court. As for the procedures for unregistered marriages, this is to be referred to specialists; therefore, consult a trustworthy lawyer.