I actually accidentally put a nylon on a wood axle recently.
It was not intentional, grabbed a rando generic string from my box of rando generic yo-yo stuff, assuming it’d be typical poly, and crazily enough it was nylon. I thought it might be when installing it, as it was super slick, and sure enough when I singed the cut end so it wouldn’t fray… that distinctive nylon stank. 
Surprisingly it… didn’t… suck? Way bouncier than I wanted initially, but once I adapted it was kinda shockingly decent. Still vastly prefer poly though on wood axles, as cotton and me do NOT get along.