The only way that Whatsapp let you back up your chats is using by linking a Google account, but I’m not sure is there’s some workaround like a third parties apps that let you back up your chats.
I know that using a third parties apps to this purpose is unsafe, but I’m just giving an example.
I managed to back up my chats and then restore it after flashing a custom ROM (so technically “another phone”) that way. it just copies the entire app with all its settings and contents and then lets you restore it to that previous state.