Short answer
A single tiny lick of ripe papaya flesh is perfectly safe for your cat. The bigger concern is the seed — while one seed is unlikely to cause cyanide poisoning due to the trace amounts, it could pose a choking hazard or cause mild stomach upset if swallowed. Remove any remaining papaya and seeds from reach. Watch your cat for any gagging, coughing, or changes in appetite over the next day. If they seem completely normal, there's no need to worry, but always remove seeds in the future.
Papaya — Food safety facts
Safe to share · Cats · full breakdown on the linked food page
Ripe flesh is safe and gentle on the stomach. Remove the seeds — they contain traces of cyanogenic compounds.
The full verdict, portion guidance and serving notes are collected on the Papaya food facts page.