"...our ship."

The phrase "our ship" was used in TOS at least two dozen times. Here are three examples:

The Cage: "I want to contact our ship."

A Taste of Armageddon: "Mister Fox, they faked a message from the Captain, they've launched an attack against our ship."

The Enterprise Incident: "What guarantee do we have they'll beam aboard our ship once we're on yours?"