nonsurgically

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*ǵʰes-
15. Proto-Indo-European*ǵʰésōr
16. Proto-Hellenic*kʰéhər
17. Ancient Greekχείρ (kheír)
18. Proto-Indo-European*werǵ-
19. Proto-Indo-European*worǵós
20. Proto-Hellenic*worgós
21. Ancient Greekχειρουργός (kheirourgós)
22. Ancient Greekχειρουργῐκός (kheirourgĭkós)
23. Late Latinchīrurgicus
24. Proto-Indo-European*h₂el-
25. Proto-Indo-European*h₂élisder.?
26. Medieval Latincirurgicālis
27. Middle Frenchcirurgica
28. Middle Englishcirurgical
29. Englishsurgical
30. Englishnonsurgical
31. Proto-Indo-European*leyg-
32. Proto-Germanic*līką
33. Englishnon-
34. Englishsurgical
35. Englishsurgically
36. English todaynonsurgically

From nonsurgical + -ly or non- + surgically.