Welcome to the Forums and the world of Vintage Airstream ownership!
What you are proposing is familiar to many of us who have retrieved Vintage Airstreams; I know that I have gone through the drill twice. In each case the tires were weather checked, but were carefully checked during the bearing/brake inspection for obvious weak spots, splits, etc. My method was to fill the tires to 90% of the maximum inflation pressure posted on the sidewall. I kept my speed low (45 MPH or less), and stopped at each opportunity to check tires and hubs for evidence of excess heat or other issues. In both cases (Overlander and Minuet), my distance was a bit greater than what you are facing - - 175 miles with the Overlander and 200 miles with the Minuet. I wasn't as concerned with the Minuet as the tires could be traced to having been installed just short of six years prior to my purchase - - the tires on the Overlander were of indeterminate age.
Something that you didn't mention, but of which you may not have yet discovered is the distinct possibility that you will find the umbilical cord needing to have its Bargman connector rewired to match your tow vehicle. In 1971, Airstream utilized a wiring schematic
that is different from the industry standard wiring schematic
that is likely utilized on your tow vehicle. My suggestion would be to carry a new trailer end to match your tow vehicle and be prepared to rewire the trailer to match your tow vehicle (the trailer wires will need to be matched to the new plug based on function rather than color as Airstream's colors for the period do not match the functional colors used in modern connectors).
Good luck with your Sovereign!