Never heard なにの. In general, when you combine NANI with a particle like NO or with DESU, you say/read it as NAN. If after NANI there`s the particles WA, GA, MO or WO you read as NANI. If after NANI there`s the particle NO or DESU or a counter like JI or SAI, you combine them and read as NAN. Ex: 何の先生ですか。(Nanno sensei desuka) - What professor?/ What kind of professor? これはなんですか。(Kore wa nandesuka) - What`s this? 何を料理していますか。(Nani wo ryourishiteimasuka) - What are you cooking? 君は何さいですか。(Kimi wa nansai desuka) - What's you age? Back to your question... NANNO and DONO both can mean "what's this/that" or "what kind/sort is". And about your sentence, it's sounds more natural to me to read as NANNO, but that because I'm more used to it, but nothing wrong with DONO too.

なんのほん です。