Fail to finish the color-changing potion?

Is it possible to not finish the teeth-whitening potion?

It seems implied, based on the achievements and general setup of the quests that there are three optional quests in the game - one for each of the townsfolk:

Help Amaya the blacksmith prevent wolves from getting into the city. Help Wente the baker not get stung by bees on his romantic picnic. Help The Hobblepots finish their teeth-whitening potion. These three tasks, when completed together, gain you the Helping Hat achievement.

...and, it seems that each of these acts changes the ending screen, as do all of your major decisions in the game:

Preventing the wolves from entering will show an award patch on Amaya. Preventing Wente from getting stung will show him without big welts on his face. Finishing the potions for the Hobblepots will show gleaming sparkles by their teeth.

However, this pattern seems to have a contradiction, as it seems impossible to complete the game without finishing the potion.

The potion is used to bypass the hypnotic powder during the Duel of Wits at the end of the game.

As such, I cannot determine any way to fail this particular quest. The other two can be failed, so I figured that this one could be too, but there would need to be some sort of alternate solution to the puzzle mentioned.

Is there a way to beat the game without completing the potion?