In Diablo 3, your loot chest, Blacksmith and Jewler are linked to your account, not your character.
If you log in from a differant character, they will all have the same recipes and levels.
Put all the reagents in your chest, and log in to a character with the corresponding primary statistic:
- Dexterity: Monk, Demon Hunter.
- Intelligence: Wizard, Witch Doctor.
- Strength: Barbarian, Crusader.
You should find that you can make the required ring from your blacksmith, even on a newly-created level 1.
I am also pretty sure that you can craft with materials that are still in your chest, so you probably just have to put the materials in the chest, and won't have to bother withdrawing them into your new characters inventory.