It's honestly a shame Rina already has an
amazing weapon in the form of her Pale Scepter mace, formerly Baelor's Warrior-blessed weapons, now sanctified to the Old Gods. It's simply too thematically fitting not to have given to her.
If we didn't have that then the Ancient Wight Lord's sword would have been the best fit. Since it's Blue Ice it already has an innate bonus to all slashing damage, but it probably has some great enchantments on it as well.
And its armor... I am cackling at what its armor might be.