[71swb4x4]

IMO you have no reason to worry about the VIN. If you do this swap, you have a LWB truck that you converted to SWB by using a SWB frame.
If you sell the truck as a factory SWB, because the VIN doesn't say it's a LWB, that is unethical, and maybe fraud.
Your SPID does tell the wheel base. You would have to have a new SPID printed, and that action alone could be viewed as fraud, if you don't disclose what you did.

You VIN on your frame and cab won't match either, and you will want to keep paperwork for both vehicles so that there isn't any questions as to whether something was stolen or not. Some states check all of the VIN numbers when registering a truck.

I am not calling you a fraud, or thief, I am just pointing out the bad side of things. People swap over LWB to SWB often, and I see nothing wrong with it as long as they aren't advertising them as "factory" swb trucks.

At the end of the day I think it would be cheaper to by a SWB truck. By the time you swap, find a bed, have things painted to match, I think you will have more time and/or money into it than you think.