Hi Rafal,
I think I get roughly what you are trying to say but with the apparent typos/slightly unclear language I’m not completely sure. I suspect you may be misunderstanding how links work.
If a recording is uploaded, it’s either public (in which case it’s listed for others to see) or it’s hidden meaning that those who have the link can view the recording but it is not listed (this is how it works because there’s no viewer authentication I believe)
See here where it mentions the secret links: Do I have to upload my recordings to asciinema.org?
If what you’re saying doesn’t fit with the above, then perhaps it’s best to show some more details, perhaps trying to recreate it with a video you don’t mind others actually seeing
Kind regards,
Neil