In that sense, it is the executor's decision and will to be the executor. Were it not his will, he would not act as executor. However, it is in the hands of the executor to allow another's will to be his own. The executor then becomes nothing other than that of a servant. The question would then become, "Does the servant honor his master's wishes?"
Truly, it is not his wish. No matter what, the executor acts in accord to what he serves. Whether he serves "the will" of some other person, or the will of his own, or even another's will that is different from the one he should execute, he is executing.
All are servants to something or someone. Whether it is to oneself or to something or someone else, all serve. An executor must execute, else he is not an executor.
ANOTHER WAY OF LOOKING AT IT...
Yes, an executor may not believe in what he is doing. He may disagree with anything and still do it.
Should a person do something that he or she should not believe in? Should a person do something with which he disagree? One must ask why he disagrees with it. If he truly does disagree with it, then should that person execute? One should always stand up for what is good and right, so it makes sense that if there is any injustice in an execution that the executor should in fact not execute.
To come back to the point, an executor may disagree with the will. He should not in good conscience, execute if he, in fact, did disagree with said will.
Thank you and good night.