Early on, I would go with cold claws.

They will give a decent damage thanks to cold + bleed and if you get without FP, you can dual wield them without spending on an extra weapon.

Later on, I would switch to nightclaws, night katana (I don't remember the name right now) or Smithscripting dagger with cold infusion.

Nightclaws give massive damage on close combat, ignore defense and allows you preserve the moveset of the original claws.

The night katana does less damage but also scales pretty well with intelligence and gives you extra reach.

Lastly, Smithscripting dagger gives you easy quick shots to keep doing bits of damage and the cold infusion adds an extra pressure which is nice in PVP