Exclude entries from search results in KMS depending on their category

We are working with one KMC and several KMS environments. Mostly the entries are published by the regular users in KMS. In some cases these same entries will be published to other KMS categories by the KMC admin.

So KMS supports only one publicity level and the end user wants to have an unlisted video (to share e.g. to stakeholders without logging in). In addition this same entry will be published to an internal category in the same KMS by the KMC admin. This creates a situation where this unlisted video will show up on the search results even to the anonymous users.
I believe this is due to "For content associated with more than one category, the privacy and visibility of this content via global search or a direct link to the video page, is determined based on the category with the lowest restriction level the content is associated with (within the application category tree)."
So the video is “public” with the unlisted setting and the category setting produces this searchable entry.

How could we modify this global KMS search so that it doesn’t search these unlisted videos (kms1 > unlisted)?
Or any other suggestions on how to solve this issue? Basically we need an option where we can share an internal entry with hidden link also.