I only own a MacBook Pro, how do I change my Apple ID as my email is changed?

I have moved away from my ISP and was using their email as my primary email address for my Apple ID. I do not own anything but a MacBook Pro. When I try to change my primary email on the MacBook through settings, it says I must use FaceTime or iMessage but neither let me set a primary email or remove my old email. I can uncheck my old email, but that doesn't change anything on my apple account. Through https://account.apple.com, it says I must change it on the MacBook.

[Edited by Moderator]