The Martial Arts feature replaces the damage die/dice itself
The monk's Martial Arts feature says:
At 1st level, your practice of martial arts gives you mastery of
combat styles that use unarmed strikes and monk weapons, which are
shortswords and any simple melee weapons that don’t have the
two-handed or heavy property.
You gain the following benefits while you are unarmed or wielding only
monk weapons and you aren’t wearing armor or wielding a shield:
- You can use Dexterity instead of Strength for the attack and damage
rolls of your unarmed strikes and monk weapons.
- You can roll a d4 in place of the normal damage of your unarmed
strike or monk weapon. This die changes as you gain monk levels, as
shown in the Martial Arts column of the Monk table.
As it says, you can roll a single d4 as your damage die (changing to a d6, d8, etc. as you level up). It does not keep the number of your existing weapon; it just replaces it. (The druid cantrip shillelagh works the same way.) This is true regardless of the weapon's original damage dice or number of damage dice.
Chris Starnes' answer further elaborates on this fact.
...But double-bladed scimitars can't be kensei weapons
The Way of the Kensei's Path of the Kensei feature expands the list of weapons that count as monk weapons for you (XGtE, p. 34; emphasis mine):
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.
Unfortunately, the double-bladed scimitar (WGtE, p. 73-74) doesn't qualify as a kensei weapon, because it has the "special" property (in addition to the "two-handed" property), and describes it below:
Special. When you take the [A]ttack action and make a two-handed attack with a double-bladed scimitar, you can use a bonus action to make a melee attack with the blade at the opposite end of the weapon. This attack uses the same ability modifier as the primary attack. The weapon’s damage die for this attack is a d4, and it deals slashing damage.
Because it has the special property, the double-bladed scimitar can not be chosen as a kensei weapon. As such, the Martial Arts feature doesn't apply to it (nor do the monk's other features tied to monk weapons).