Does Hircine Ring Work Without Lycanthropy?

The Ring of Hircine does not automatically make you a werewolf: it just grants you the ability to transform one additional time per day¹, but only if you already have lycanthropy. The only way to contract lycanthropy is to seek out the Companions.

Can you use the ring of Hircine without being a werewolf?

Without mods, no. You must already be a werewolf to gain any benefit from the Ring of Hircine.

Can you keep the ring of Hircine?

It is possible to keep the Cursed Ring of Hircine while still getting one or both of the final quest rewards. After defeating the hunters and talking to Sinding, the quest will be considered complete, and the Cursed Ring of Hircine may then be dropped or stored, as it is no longer considered a quest item.