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=\"}