I'm not sure what you mean when you say hand carved "classic American hunting rifle." If you mean decorative carving such as a floral pattern this would not be classic "American" but rather German or Austrian. If carved means custom stocked than there are features that are classic American. Everybody has a different view of the term classic but in general it would be a high flat comb, moderately open pistol grip, small to medium sized forearm and checkered grip and forearm. Go to GUNSAMERICA and search for Dakota Firearms. The bolt guns termed Classic generally have stocks in the classic American style. Additional refinement might include Ebony forearm tip, skeleton buttplate, skeleton grip cap, shadow line cheekpiece, high LPI checkering with fleur-de-lis pattern, inletted sling mounts, etc.
You probably already know that the grain in the wrist needs to be straight but it bears repeating. There are lots of different walnuts and though Claro can have gorgeous grain it is not the ideal wood for high LPI checkering as it is somewhat brittle. Stocking, at it's best, is an art form and the cost is commensurate. A little more info., regarding what you are trying to accomplish, would help in providing suggestions.