Can a Mithral Great Sword be used as a Kensei Monk's Kensei Weapon?

Question

Can a Mithral Great Sword be used as a Kensei Monk's Kensei Weapon?

If Mithral is a light weight material for armor....can it work with weapons? Meaning would a mithral great sword negate the heavy property?

Kensei Weapons. Choose two types of weapons to be your kensei weapons: one melee weapon and one ranged weapon. Each of these weapons can be any simple or martial weapon that lacks the heavy and special properties. The longbow is also a valid choice. You gain proficiency with these weapons if you don't already have it. Weapons of the chosen types are monk weapons for you. Many of this tradition's features work only with your kensei weapons. When you reach 6th, 11th, and 17th level in this class, you can choose another type of weapon—either melee or ranged—to be a kensei weapon for you, following the criteria above.

Answer 1

Kensei choose weapon types, not specific weapons.

Choose two types of weapons to be your kensei weapons …

“Mithral Great Sword” isn’t a weapon type; “Greatsword”, “Longsword”, “Club”, etc, are weapon types.

Also, of course, there are no rules for mithral weapons. The descriptions of mithral used for armor say that mithral is “is a light, flexible metal”, and lightness and flexibility aren’t typically desirable features of a greatsword.

(More generally, if you want a “light greatsword”, there’s always the longsword).

Answer 2

RAW: Unfortunately No

From description of mithral armor from DMG:

Armor (medium or heavy, but not hide), uncommon

Mithral is a light, flexible metal. A mithral Chain Shirt or Breastplate can be worn under normal clothes. If the armor normally imposes disadvantage on Dexterity (Stealth) checks or has a Strength requirement, the mithral version of the armor doesn’t.

Nothing in the description says weapons made of mithral are not considered heavy. Even more, this variant (because mithral is a variant to "normal" resource used to make items) does not even specify what benefits it would give if weapons are made of it, if any. After all, this is a armor variant.

You can argue that, per description and common sense, weapons made of it should be lighter than normal, and they certainly will be. But that does not mean weapon itself will stop being "heavy", or lose heavy property. If that would be the case, heavy armor would stop being heavy, because "it is lighter", which is not the case, as per RAW.