I haven't come across the answer to this anywhere, but can I level my werewolf skills if I use the Ring to transform, or do I have to transform naturally, first?

How you transform has nothing to do with it. You earn "points" in order to level by eating your humanoid victims. When you have enough points, you can access the skill-up tree while in werewolf form and choose perks.

But sometimes there's a strange delay between eating your victims and the message that you have perks available. This delay is usually so long that you've transformed back to a person by the time you get the messages.