I have found various cheapie Chinese/Indian wooden or bamboo whistles with quite nice tone, but the scales vary considerably from standard. If you find one that is in tune, it needs a better finish inside and out, and the end wrapped to last, also some sealer on the bit to keep it from getting soggy.

My grandmother said it this way:
"I bought a wooden whistle,
but it wooden whistle,
and I bought a steel whistle,
but it steel wooden whistle,
So I bought a tin whistle,
and now I tin whistle."
Blessings,
Barbara