shiranai (shirimasen) and wakaranai (wakarimasen) both can mean "I don't know" but there's differences shiranai is closer to 'I'm not familiar with something' or 'I'm not aware of something' wakaranai is closer to 'i don't understand / I don't know right now' so if someone asks you if you're going to go to a party, you might use wakaranai because you don't know at the moment but you know about the party. and if someone were to ask you if you knew your friend had a baby, you might use shiranai in that case in any case, its not nan desuka

Shirimasen = negative form of "shiru", to know.

shiranai=I don't know. wakaranai=I don't understand.

知らない です(shiranai desu) is a simple way of saying you dont know

Shirimasen or wakarimasen. I think in certain contexts nan desu ka could be loosely translated into I don't know. Just like in English "what's that?" Means I don't know it. But I think you're right and he's wrong.