I would not want a remake of Voyager, HOWEVER this is all in good fun and I don't care about what the budget may or may not be. So, here is my would-be cast. Like I said though, I love Voyager as is and think a cheesy remake would be pretty lame at this point.
Captain Janeway: Kate Winslet. British Janeway!
Chakotay: I'll agree with Adam Beach.
Tom Paris: Seann William Scott or Ryan Reynolds.
B'ellana Torres: Halle Berry
Harry Kim: John Cho is my first pick, but he's 40 now...too old to be Harry. Randall Park is my second, but also a little too old. Maybe either one of them could get away with it if it were like 5 years ago.
Seven of Nine: Stephanie March for 7. Strong, fierce, blonde. She wouldn't be as "sexy" in a catsuit, but I think she could play a Human/Borg trying to regain her humanity no problem.
Tuvok: Lee Thompson Young
Neelix: Jack Black. LOL
Kes: Dakota Fanning
The Doctor: Steve Carell, Hugh Laurie, or...just keep Robert Picardo.