I found this on the ATF website, this brings up a very interesting point..
The definition for curio or relic (“C & R”) firearms found in 27 CFR § 478.11 does not specifically state that a firearm must be in its original condition to be classified as a C&R firearm. However, ATF Ruling 85-10, which discusses the importation of military C&R firearms, notes that they must be in original configuration and adds that a receiver is not a C&R item. Combining this ruling and the definition of C&R firearms, the Firearms Technology Branch (FTB) has concluded that a firearm must be in its original condition to be considered a C&R weapon.
It is also the opinion of FTB, however, that a minor change such as the addition of scope mounts, non-original sights, or sling swivels would not remove a firearm from its original condition. Moreover, we have determined that replacing particular firearms parts with new parts that are made to the original design would also be acceptable-for example, replacing a cracked M1 Grand stock with a new wooden stock of the same design, but replacing the original firearm stock with a plastic stock would change its classification as a C&R item.
So it appears that you cannot change stocks unless it's the original type.