Restore to an old iphone while waiting for next iPhone model to come out

All,

My iPhone 8 died hard and I’d like to wait and get the next version of the iPhone since it should be coming out in a couple months. Can I restore the last successful iCloud backup for my iPhone 8 to my old iPhone 6 (or it might be a 5)? The iCloud backup is old because I ran out of space but it should be good enough. And does it need to be an active phone (do I need to activate it with my phone number via T-Mobile/ATT/Verizon?). I just need some of my notes off of it even if it might be 3 months old.

Note: I do not have a computer. Just an iPhone and an iPad.

Thanks in Advance