Read the card text again. Dakini doesn't target, it makes you select(your choice). It's all indirect, it's kinda hard to explain but that's how the ruling is.
But it's write "this card is unaffected by other monsters' effects", which means any monsters effect should not work on him, but it would make more sense if it was something like "he cannot be targeted by mosters effect". I understand this, but I think the text is wrong.
Fisherman II's effect only protects itself and not you, therefore Dakini's effect bypass the protection since Dakini's effect affects you and not Fisherman II.