I know it seems a pain - but you'll find it's not that bad once you get started.

60-68 wouldn't take that long. Boost the shammy through ramparts, blood furnace and the various coilfang instances.
At 68 take it to northrend, get to 70 and earn a big chunk of gear upgrades in no time.

I guess quest 70-71. Then hop into BG's for 71-80. Plus you'll be able to take the shammy through northrend instances on normal with the group.

If you get bored - swap on to your other team and work on them to remind yourself why you want to replace that hunter