I am sure this subject has been discussed before but here goes:-
Many years ago a very well known and great Northumbrian whistle player called Bill Conroy, advised me not to use a trembling finger above a hole to produce vibrato as it would spoil my style of playing. I use my throat breath to do this instead. However, I notice that all the good whistle players I see and hear invariably use the finger technique.
Then I read a criticism of Finbar Furey supposedly using breath vibrato when playing his Lonesone Boatman. Surely it is just a personal choice and if the end result is pleasing……? I fear I might have answered my own question, but it would be interesting to hear what others say.