There are a few things that you will have to do to successfully transfer your User Shapes from one Catalog to another (that's the first step). Then getting them into your new Project and related Specs (the second and trickier step).

Getting the Catalog up to date:
First you will need to use the Transfer Catalog Data tool to transfer your User Shape data files from your old catalog to your new Catalog.

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Next you will need to move/copy the User Shape folder from the earlier "Spec" folder location to the new "Spec" folder location.

Getting the User Shapes from old Spec/Project to new Spec/Project:
Use the Transfer Project Data tool to transfer your spec(s) from the old to new project (PRJ).

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Using the Properties panel in CADWorx Spec Editor to select the "new" catalog as the spec will retain the original catalog and path.

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Since the data table exists in the new catalog, there should be no problems with redefining the "correct" catalog.