Speaking as a local* - I think your first route is both shortest, and most pleasant. In all three cases you have to get out of crewe, and the distance to do that is the same
After that the main crewe nantwich road (534) is actually quite nice, going through niceish 'burbs and villages. It is also relatively quiet, since it has effectively been bypassed for the heavy traffic by the A500.
*when I was a kid, the 534 was my route from home in NE natntwich to the model/bike shop at the SW end of crewe. Tis where I got my first bikes, and the replacement frame when I bent one cycling into the rear of a parked car.
EDIT: I've just noticed your end point is 1/2 mile from the last house my parents had before emigrating to USA (Dig Lane)