There isare indeed no weapons that fulfill your requirements.
List of all reach melee weapons:
- Glaive (Heavy, Two Handed, Reach)
- Pike (Heavy, Two Handed, Reach)
- Halberd (Heavy, Two Handed, Reach)
- Whip (Finesse, Reach)
- Lance (Special, Reach)
This is likely intentional, reach is a powerful tag in 5E allowing for a lot of battlefield control especially combined with feats like Sentinel.
If you are interested mostly aboutin the aesthetics of the character rather thenthan the mechanics, I would suggest working with your GM and creating a custom weapon. The DMG provides some guidance in that area.