I don't think Chakotay ever agreed with Janeway, exactly, in this one. I think it was more of a case that, as first officer, he had to back her orders in front of the crew.this is *the* one and only time Chakotay actually stood up to Janeway... and still got sucked in to agree with her.
I think he handled the whole thing very professionally, really -- question her decision in private, but never let the crew see that their leaders were in disagreement. Which was was why it galled me when she did that whiny "Then I guess I'm alone," bit, because wow, way to take it personally, Captain.