I think that only Zoro and Nami would be dead weights. Due to having greater strength, Zoro would still be handy as a deckhand (setting the sail, pulling ropes, carrying cargo, etc.), so Nami would be dead last. lol
Here's my ranking:
1. Luffy: he would still be 1st, as he's the strongest of the crew and still would be able to act as a combatant;
2. Sanji: either him or Zoro would assume the captain's position; the decisions would be more level-headed if Sanji becomes the captain and he would still be one of the strongest combatants;
3. Robin: as she sailed the Grand Line on her own for a good time and probably had the most experience with crews, she's probably knowledgeable about things like cooking, navigation, first aid, etc. And she's also a good fighter.
4. Jinbe: one of the strongest combatants too... and he's also a top porter. lol
5. Franky: he's an inventor, so he could be some sort of scientist on the ship... and he's also a good fighter;
6. Usopp: he would still be useful with his engineering (jury-rigged shipwriting and some sort of inventions like the clima-tact) and pop greens... he just wouldn't fight anymore;
7. Brook: he was the helmsman before Jinbe, so I'd guess that he would assume the role again with Jinbe out... plus, he's also a good fighter;
8. Chopper: if he can be a pharmacologist/chemist, he'd go up as #5 (above Franky imo)... otherwise, he would just help as a deckhand and as a fighter too;
9. Nami: would probably help as a deckhand and as a fighter too, but as she's one of the weakest fighters, it wouldn't make that much of a difference;
10. Zoro: he would be a deckhand only. Maybe would assume the captain's role, but I'm not sure if his decisions would be that much better than Luffy's. lol