1) In edit mode, go to your vertex settings (it's the triangle connected with vertices icon) and click the plus sign to add a vertex group. Rename this vertex group something like "shrink".
2) Select all your vertices (Hotkey "A") and then in the vertex group tab, click "Assign".
3) In your Shrinkwrap Modifier, add this vertex group.
4) Then, select only the vertices you don't want shrinkwrapped to your original.
5) After that, with those vertices selected, in the vertex tab and with the vertex group selected, click "Unassign". Those vertices will be excluded from the shrinkwrap.
Hope you can understand my explanation and good luck with it :)