It is possible to control which cookies the player can set using the REST API and the  allowedcookies parameter.

An option is to fetch a completely cookieless player by setting the parameter an empty sting:

curl "https://rest.screen9.com/123456/videos/DqCsvA8McDeg1onWaRz_Mw/embed?allowedcookies="

This would result in a response similar to:

{"id": "DqCsvA8McDeg1onWaRz_Mw", "embed": "<iframe allow=\"autoplay; fullscreen\" allowfullscreen height=\"360\" referrerpolicy=\"no-referrer-when-downgrade\" src=\"https://api.screen9.com/embed/I-X52hrJNsre-ksyzeF_ni2kbjGeWwlQx8My3eREoqw?allowedcookies=\" style=\"border:0;\" title=\"bunny lo-res\" width=\"640\"></iframe>"}

Such player can be then instructed to store more cookies depending on user preferences as described in Setting player to store only allowed cookie article.

A Screen9 account can also be set up to prevent Screen9 Player to store any cookies. Please contact support if you want to have this enabled.