There are two options here with very different ramifications
Unused damage dice do not trigger OVERKILL
In this scenario you would roll 4d6, and choose the two highest, completely ignoring the other two dice. This is somewhat supported as the Critical Hits section says
[...] On a critical hit, all damage dice are rolled twice (including bonus damage) ...
Cutting Words modifies the d20 roll, and modifiers don't cancel critical hits
The steps for making an attack are described as follows (emphasis added):
Whether you're striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.
Choose a target. Pick a target within your ...
The rules use a certain pattern when discussing modifiers and Cutting Words adheres to that pattern. It is therefore a modifier to a roll result and does not replace the result.
Almost without fail:
If a modifier is a fixed value, the rules use the words "modifier" and "penalty."
See Raise Dead, Resurrection, Slow, Alter Self, Haste, Magic Weapon, ...
Cutting Words is not a bonus or modifier, it is subtraction from a roll
This is unique language. In 5e subtract is only ever used in the normal English sense, it is never used to refer to the game terms "bonus" or "modifier".
For example, when explaining passive disadvantage:
For disadvantage, subtract 5
When explaining ability modifiers:
The rules for making an attack state:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. This is called a critical hit, which is explained later in this section.
If the d20 roll for an attack is a 1, the attack misses regardless of
any modifiers or the target's AC.
So if a player is making the ...
You can use the feature until the DM declares the result
The intent of this features is to be used between the rolling of the dice and the DM declaring the results. If there was meant to be special behaviour on a 20 or a 1 the features would say so.
Natural 20's can still miss
It is possible for there to be situations where a natural 20 is not a ...
You can still miss on a 20, and you can still hit on a 1*
Even if you see the 20 or 1, the attack isn't resolved and you cannot be 100% sure of the result. The rules state that a 20 or 1 only ignore AC and modifiers, not anything else:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC.
If the d20 ...
If you roll a 1 or 20 on an attack roll, you know whether it hits or misses
Since a 1 always misses and a 20 is always a (critical) hit, if you see those numbers, the result is known. Therefore, you cannot use any ability that requires you not to know.
Don't overthink it. The surprised state ends when the DM determines it ends - the narrative at this point has precedence over stark combat rules, here in this grey area just before and just after initiative is rolled. The DM, if he is any good, should consider your description of your stealthy approach, mitigating environmental factors, the rolls you made ...
The Dungeon Master's Guide has rules for handling this case:
On the Monsters and Critical Hits section (DMG page 248), it states what to do in the case of a monster critical hit when using average damage:
When the monster scores a critical hit, roll all the damage dice associated with the hit and add them to the average damage. For example, if a goblin ...
Are there official rules on this?
Yes, per Sdjz's answer..
But it requires a die roll.
You can do it without any dice rolling if you like.
What have I seen done that is fast and simple?
A critical hit when using average damage is "Max roll +1"
If I am doing 1d4, it becomes 5 + modifier.
If I am doing 1d6, it becomes 7 + modifier.
Easy to keep ...