The way I see this is that each state would need to allow non-residents to get permits(or reciprocity). A visitor to another state should be able to be treated just like a resident(exceptions would be voting and welfare of course). The offending states in regards to CCW are NY and CA, which normally won't issue to non-residents. There are others, like SC and CO, which don't issue to non-residents and only accept certain other states permits. That should be a violation of the P or I clause of the 14th Amendment.
See Ward v. Maryland 1870 for a successful case involving the P or I clause.