There are 2 ways you can handle this, one simple and one more complicated.
1. Simple - create a search group (Products > Taxonomy > Search Groups), and manually add the products you want to show. There can be any number and they can be any products you want. The link will then be just search_group_code=XYZ. For instance, if you create a group called "custom_shotguns", it would be https://YourClientURL.com/product-search-results?search_group=custom_shotguns
The disadvantage of this is that products have to be added manually and won't stay up to date with whatever matches the criteria you want to use (e.g. 20 GA semi-auto shotguns).
2. More complicated - figure out what search parameters you want to use and construct a URL that includes them all. Departments, categories, etc. are simple, but facets are tricky. You would have to identify each product_facet_option_id that you want to include by inspecting the source of the page. The URL will be something like this:
Shortening that URL into something simple could be done outside coreFORCE (with a tool bit.ly) or as a URL alias in coreFORCE. "Old URL" is something like https://YourClientURL.com/custom-shotguns and the "New URL" is the link above (once all the required parameters have been figured out).
This will stay up to date with current search results, but the disadvantage is that the display on the page will not be very detailed. The page title will probably just be one of the manufacturers and all the search criteria will not be displayed on the sidebar. That is probably a bug that can be fixed if you decide to proceed with this option.