Not sure what size has to do with it! It needs locking up if your KH says it needs locking up. Simples.
As a submissive to serve your mistress properly your cock should be locked, if your her slave then absolutely in must be locked is my understanding. There should be no self gratification as a submissive unless supervised, my ex KH wouldn't allow me even to touch my unlocked cock without supervision, it was her property. As a slave you have no choice I'd have thought, as mistress watchful has stated it's up to your KH.
A cock under 4 inches can be used for masturbation, an if the desire of a Mistress (or Master) is that masturbation is controlled, then that cock should be locked up.
I agree with @Mistress Watchful size is irrelevant, the locking of ones penis is a symbolic gesture of devotion and trust between two individuals. True the majority of submissive have under endowed penises but this doesn't mean that more 'blessed' men cannot be submissive or indeed locked in chastity.
I would agree with the others. Lock it up. I LIKE being locked up. I love to show my Goddess how much I love her and am loyal to her by being locked up. Size does not matter; it’s the demonstration of feeling that counts. The fact that one person is willing, even enthusiastic to hand themselves over to somebody else. Some people wear a wedding ring to show commitment, I am happy to wear a chastity belt to show commitment & Love
There is also the argument that it should be locked up because it is so small! It is of no use to anyone is it!