Axle length is how long the threaded axle upon which the hub sits is.... the axle length needs to be long enough to account for the space between the dropouts, and still leave enough space for the axle nuts. Typically, the 148mm Sturmey-Archer hubs are available in 28h only, and are spaced at a very narrow 108mm. The 163 will be spaced at 117 or 118 from the factory. The 175mm will be spaced at 126mm. These figures represent the space taken up by the hub, between the "locknuts", on the axle, and should correspond to the space between the dropouts on your frame. With most hubs, the spacing can be increased by adding spacers; in some cases, there will be spacers from the factory that, once removed, will reduce the spacing. With "normal" hubs, axles can be changed by cutting them down, but most Sturmey-Archer hubs have an axle that is hollow on the driveside, and gears are changed by a chain within the axle, so you wouldn't want to cut a Sturmey-Archer axle. You can swap axles, but be prepared to spend a lot of time/effort getting the adjustment of the hub itself right after an operation like that.
If I were you, i wouldn't buy a hub until I'd settled on which EXACT frame i was going to use, so I could select the hub that best fit my needs. Make sense?