Is it permissible to wash the inside of a ritually impure winter shoe in an automatic washing machine, and would that be sufficient, given that the opening of the shoe is narrow?

The method of purifying a shoe is by removing the impurity itself, pouring water over its location until its color, taste, and smell are gone. If washing the shoe in an automatic washing machine removes the impurity, then it becomes pure by that. It is advised not to succumb to obsessive doubts.