Your logic is something like this:
Sneak Attack […] The attack must use a finesse […] weapon.
(Player’s Handbook, pg. 96)
Finesse. When making an attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the attack and damage rolls.
(Player’s Handbook, pg. 147)
Kensai Weapons. […] Whenever you wield a kensei weapon, you choose whether to use Dexterity or Strength for the attack and damage rolls of the weapon,
(Xanathar’s Guide to Everything, pg. 34)
⇒ “kensai weapons are finesse weapons” (alleged implication of 2 & 3)
⇒ “kensai weapons can be used for sneak attack.” (implication of 1 & 4)
The problem is in the jump from 3 to 4:
- “kensai weapons can use Strength or Dexterity” ⇏ “kensai weapons are finesse weapons”
This logical implication is not supported by your evidence (and indeed, evidence supporting it is not in the rules at all).
What you have is a statement that
- “X is a finesse weapon” ⇒ “X can use Strength or Dexterity” (equivalent to 2)
but what you want is the “converse,” that
- “X can use Strength or Dexterity” ⇒ “X is a finesse weapon” (6 “in reverse”)
But you cannot logically reverse an implication like that. The reversed statement is known as the “converse,” and a statement and its converse are not logically equivalent. This kind of logical fallacy is known as a “converse error” (or “affirming the consequent” or “fallacy of the converse” or “confusion of necessity and sufficiency”). You cannot determine whether or not a converse is true from the original statement.
In other words, just because all finesse weapons can use Strength or Dexterity, does not mean that all weapons that can use Strength or Dexterity are finesse weapons.
As an example, consider this:
- “X is a finesse weapon” ⇒ “X can be used for sneak attack” (equivalent to 1)
This is a true statement, a rewording of what I quoted from PHB pg. 96. Now consider its converse:
- “X can be used for sneak attack” ⇒ “X is a finesse weapon” (converse of 8)
We know that this statement is not true. Because page 96 actually says “The attack must use a finesse or a ranged weapon,” so “X can be used for sneak attack” could mean X is a finesse weapon—or it could mean that X is a ranged weapon. Just knowing that X can be used for a sneak attack, and knowing the rule on page 96, is not enough information to decide whether or not X is a finesse weapon. We need another statement—like “X is not a ranged weapon,” or even something like “all weapons that can sneak attack are finesse weapons [yes even the ranged ones]” (which wouldn’t make a lot of sense in the context of the game but wouldn’t be any kind of logical problem), in order to answer whether or not X is finesse here.
Likewise, knowing that kensai weapons can use Strength or Dexterity is not enough information to say they are finesse weapons: you need an actual statement saying that they are finesse weapons, or that all weapons that can use Strength or Dexterity are finesse weapons, or something. Unfortunately for you, the rules don’t provide any such statement.