This is a very good question, which has been fully addressed in בני בנים ג:ו
ד"ה עוד קשה לי httpsבני בנים ג://www.hebrewbooks.org/pdfpager.aspx?req=20024&st=&pgnum=26&hilite=ו
ד"ה עוד קשה לי by by Rav Yehudah Herzl Henkin, who concludes that nails do not actually pose a problem of tumah.
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