Is the nephew obligated to carry out his uncle's will by marrying his daughter, despite his desire to marry another, and is he sinful if he does not do so?

It is not obligatory to carry out the father's will regarding the marriage of his daughter to a specific person. Neither his nephew nor anyone else is sinful for not executing this will. However, if the young man is able to marry his cousin, it would be better. If that is not possible, perhaps there is good in it, and "Allah knows, and you do not know."