Deterministic nonces in CTR mode
Assuming that you can indeed guarantee that the keys will never be reused, both schemes should be secure.

The only requirement for the nonce in CTR mode is that it must be unique (and, if used directly as the initial counter value, not equal to any intermediate counter value used in the past or in the future).  If you're only encrypting one message with a given key, the nonce $0$ is as unique as any other.

As you correctly note, your second scheme provides somewhat less information to an attacker who can guess some of the plaintext.  (Reading between the lines in your question, I'm assuming you're not planning to store the nonce along with the ciphertext, but to re-derive it from the master key on decryption.)  Whether it's "better" is hard to say &mdash; it only makes a difference if the cipher you're using is broken, and at that point it will depend on just how it's broken &mdash; but it's at least unlikely to be worse.