Yes, you could say that. "Your number is in safe hands" - direct response. "Don't worry, your number is in safe hands" - reassuring response. "No problem, I'll keep this between you and me" - conspiratorial response ;) "Don't worry, I'm not a blabbermouth" - passive\aggressive response. "Actually I was going to plaster it all over the walls, so yeah, don't worry" - sarcastic response.

yes

Yes, it is correct, but not entirely fitting, given the context. We say something is in "safe hands" when the object is entrusted to our care. Similarly, we say it when somebody trusts us to look after them or help them with something. In the case of a phone number which a person trusts you with, they are merely making you privy to that information, but it is not a tangible object for you to keep or take custody of. So, you might instead respond in a different manner; for example: - "Don't worry, I will not share your number with anybody else" ... or quite simply, "don't worry, I won't". - "You can trust me to respect your desire for privacy" - "I will not betray your trust in this matter..." Essentially, you want to tell them that they can trust you.

"Your phone number is in safe hands". "I won't give out your phone number to anyone". "You can rely on my discretion".