Just be really careful with those tires. Personally, for safety, I would put a fresh set of tires on before going on any long or fast rides. 20 year old tires I just wouldn't trust my life to.
Those tires are original - so over 50 years old! I wouldn't ride around the block on them.
Because the bike is 90% original, I don't want to take them off, so the only option would be finding another set of wheels and mount new tires on them.
I'm really picky about tires, and just replaced a set of tires that were 5 years old but still looked fine.