I was supposed to go to Cairo a month ago. Never made it due to a misconnection but based on the conversation at this link I wasn’t too concerned about the stamp issue. Sounds like they aren’t expecting it for US results. Had no problem getting BPs issued by DL in the US but didn’t make it to my actual Cairo flight so can’t say for sure that it would have worked.

https://www.booking.com/communities/...try-into-egypt