Translation:I do not want him to know our secret.
I cannot think of an example where tell=ξέρω. What I can say is that this translation should be fixed to "I do not want him/her to know our secret". That's what it means, that's why the subjunctive is in third person: I do not want an unidentified third party to know our secret.
You can still drop the pronoun and just use the third person and just imply it ;)
The difference between the two him/her is this: Δεν θέλω αυτός/αυτή να ξέρει το μυστικό μας.
However, note that when you say that in Greek, instead of dropping the pronoun for a person that is known in the conversation, it is more like saying "I don't want him/her knowing our secret", implying it's the person specific that you want to keep the secret from but you may be OK with sharing it with others.