Is it possible to replace a shape layer that has a puppet tool animation recorded on to it? Apparantly I'm not allowed to precompose the layer while "leaving the attributes" (the upper option that you normally get when precomposing just a single layer) since that option is greyed out. And when I try to alt-drag a precomposition to replace the original shape layer on the timeline I get "error 26::335 layer does not have a source". Maybe there is some third way that I could try to get the layer replaced while maintaining the puppet tool animation?
What Todd suggested will not work directly. You cannot copy the mesh. Therefore you will have to create it first on your replacement layer, then copy&paste the pins. Since the algorithm is dynamic and the mesh will look different, deformations will be different, though.