Older rubber and certainly antique rubber (10 years+) tends to have two main problems - they are very puncture prone and are subject to sudden failure. Sudden failure occurs because the tyre flexes a lot as it rotates, squishing outwards and then back as the tyre passes through the contact area. This stresses the internal structure of the tyre and essentially the layers can separate. They might not. But they can. Secondly, the wire can relax, leading to a very loose fit on the rim. I experienced this last weekend when I helped out someone stuck without spare tube or repair kit, with very old tyres on his bike. Repaired the snakebite, reinstalled the tyre, and then pumped to working pressure...suddenly out burped the inner tube and ‘GAPOW....’ a huge blasted hole in the inner tube. Oh well, fitted my new inner tube which I always carry and pumped up to a very modest pressure....
For yours...perhaps pump them up to the right pressure - see what happens.
Ride them - see what happens.
But take a folding spare.