U.S. Constitution, Article 2, Section 2, Clause 2: [The President] ...”shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;”
The operative word here is “present.” The Vice President, as President of the Senate, can and probably will call a special session of the Senate consisting of himself, Chucky Shumer, Diane Feinstein and any other anti-gun members to vote on this treaty. The special session will be held in the middle of the night on a holiday weekend when Congress is all but closed down. Think December 23 or 24 of this year.
They would still need a quorum, which would have to include, at a minimum, nine senators who are already on the public record in opposition. Preventing the rest of the Senate from attending would be quite a trick, too. And the VP, of course, would have no vote.