In my research I haven't found a genuine word for "nut" either.
I do have original words for "beans" :
Ancient Egyptian: pr(i), iwryt, 3ndr (d has _ under it)
Coptic (Bohairic) : an'sh'ipi, anGipi (species of bean comes from '3ndr')
Coptic: oupw (comes from Ancient Egyptian "iwryt")
Akkadian: púlu (possibly similar to Ancient Egyptian "pr(i)"
In Ancient Phonecian they had a word for 'walnut' = guzím
And in Modern Berber they have a similar word for 'walnut' = '(a)guzim',
Which means it passed from Ancient Phonecian to Modern Berber,
Maybe Egyptian had a similar word if it existed.
Those are the closest words I've been able to find.