I didn't use a "fairy", we just had her bag them all up and take them somewhere (not at home, but at a pre-arranged store) and she (herself) exchanged her bag of binkies for a bag of toys of her choosing.
On her 2nd birthday.
It was the bakery at the store where I had ordered her birthday cake. I had gotten into a conversation with the clerk/baker, and she suggested bringing her in to exchange then for some of the cake topper kits. Daughter settled on something Dora and a Winnie The Pooh/Piglet teeter-totter, if I recall correctly.
Easy peasy. No crying. She did this herself (made the exchange, handed over the bag--actually, she dumped them out of the bag into a huge trash bin at the end of the bakery counter). I think it was empowering for her.
She was quite proud walking out of the store with her ziploc bag of goodies she had chosen herself.
She asked about them maybe once... and I reminded her gently that she had exchanged them for the toys. She was satisfied, and that was that. The rest of the bedtime routine went on normally and there was no problems whatsoever.
She actually found one months later (that we had missed) under her bed (hidden near the wall and behind the bedskirt under her toddler bed). She came down the hallway with it in her mouth, showing it to me. I said not a word (except to ask where it came from). Found it about 10 minutes later abandoned on a bench near the front door.
Picked it up, put it up in a cabinet way in the back. The end. Never even asked me about it.
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It probably helped that she was totally in love with her stuffed animal lovey.