nonwoody

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*dwóh₁
15. Proto-Indo-European*dwi-
16. Proto-Indo-European*dʰeh₁-
17. Proto-Indo-European*h₁weydʰh₁-
18. Proto-Indo-European*(h₁)wéydʰ(h₁)us
19. Proto-Germanic*widuz
20. Proto-West Germanic*widu
21. Old Englishwidu
22. Old Englishwudu
23. Middle Englishwode
24. Englishwood
25. Englishwoody
26. English todaynonwoody

From non- + woody.