You want to have your library be on the classic, hooked to your computer as though it is an external hard drive ( and not an ipod), and then at the same time connect another ipod to the computer when you want to sync it?
I am sure it is possible, just move your itunes folder to you ipod as though you are loading non music files onto it. Then change your itunes preferences to reflect the new path of the library.
Keep in mind that ipods are notorious for having slow data transfer rates, and being very unstable in terms of reliable data storage.
A small external HDD would do the same thing, albiet faster and more reliably. An external enclosure, like
this one for $40 from Memory Express. Put in a
500 Gig HDD, for $56, or
1TB for $86 . Alternately if you have an old HDD kicking around somewhere, you could just buy the enclosure and put the old drive into it.
If the idea of putting a HDD into an enclosure bothers you, which it really shouldn't because it is very simple, you could get a external drive as a single unit.
This one from best buy is $99 for 250 gig.