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There were many other people who could have been chosen to remove the dead bodies of Nadav and Avihu from the Mishkan (Vayikra 10:4). Why were מִישָׁאֵל and אֶלְצָפָן chosen for this task as opposed to anyone else, such as the other cousins listed in Shemos 6:21.

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1) Netziv (Vayikra 10:4) says:

אל מישאל ואל אלצפן בני עזיאל דד אהרן – כבר נדרש בת״כ למאי כתיב דד אהרן. ולפי הפשט משמעות דד כמו ידידות מלשון כי טובים דדיך. ובא לפרש למה קרא לבני עוזיאל יותר מבני יצהר וכדומה. אלא משום שידע משה שיש מהם מקנאים לאהרן. וכבודו והיו נראים בזה כשמחים לאידו. ע״כ קרא לבני עוזיאל שידע שהוא אוהב וריע ומצטער בצערו. וכן היו בניו ענוים ותיקים. ומדתו של מישאל יש להבין ממה שהיה אחיו הקטן נשיא לקהת והוא לא ערער ע״ז. וגם אלצפן שמו אליצפן וכתיב חסר יו״ד לראות שהיה שפל בעיני עצמו כידוע דרכי השמות.

Within that answer he throws out 2 points to consider as to why these two in particular would be appropriate for this job:

  • Uziel was particularly close to Aharon, and cared very deeply about what had happened.
  • These children themselves (Mishael and Eltzafan) were very modest, as evidenced by the fact that Mishael did not protest the fact that his younger brother was the Nasi of Kehas, and that El(i)tzafan's name is missing a Yud here, which is an indication of modesty of sorts.

2) In short, the answer given in the link provided by Gershon Gold in the comments above is that based on Chazal (Sukkah 25b) Mishael and Eltzafan were very careful about not Paskening Halacha in inappropriate situations. Therefore, they were chosen because their behavior contrasts nicely with the behavior of Nadav and Avihu, who according to Chazal (Yoma 53a) died because they Paskened a Halacha in front of their teacher.

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