If Voyager was to lose a crew member to a mirror Voyager which was facing a space-battle who would be your candidate?
Well, that depends. If Voyager would get the crew member back after the fight, Janeway. If the crew member dies or was stuck there, Harry Kim.
Okay, I need to know that part. In that case, I'd say... Chakotay. He's a good officer. He's smart. He does well in battle, and he'd make our Voyager look good.
In all sincerity, based on what you said about "Yesterday's Enterprise", it would make the most sense. He's a warrior hero. He goes out to fight on behalf of what he believes in, and, right now (in the frame of Voy), it's Voyager and the crew. I can easily seem him going over to that other ship knowing he'd never come back if it meant protecting them and bringing the universe back into balance. He's that kind of guy.
Like Tasha before him, in order to save the crew of his ship, Harry will submit to the enemy commanders "advances."
^^^LOL, I voted for Seven. Seska would just turn the mirror universe against the other Voyager oh boy what a mess. I'm not sure why I picked Seven it's a J/C thing I got going deep down . Janeway would just try to save whoever it was anyway and she'd succeed.