You normally would let nature take its course, and then retreive the item once he has passed it out in his daily business. However with the whole thing. perhaps you should go and seek advice from your vet as you do not state if it is in bits or the whole thing.The whole thing may prove difficult to pass for a tiny puppy, it depends how old he is.
If the bits dont get lost, which means that you will not be able to identify the bits, the process should take two days.
I do not think you should worry so much as it will come out eventually

 Take him to a vet immediately. He could be in danger.