How to limit categories on Ask a Question to a single product

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We are using the ProductCategoryInput widget on the Ask a Question page.  It currently shows all of the categories in our list.  We only want a subset of categories listed here, but we want the full list of categories available for the knowledge base. If I make certain categories not visible to the user then the knowledge article using that category disappear also.

I would like to create a Product called Ask A Question and link the Ask a Question categories to it, then just show the Ask a Question categories in the ProductCategoryInput widget.

Is there any way to do this or something similar without creating a custom widget?