Stuck changing Apple ID email from work to personal

I have 2 accounts. 1 of the accounts is using a work email address which I now need to remove and change to a personal email. Trying to do it online doesn't work as it says you can't do this online to prevent stolen devices from being used so change the email address on one of your devices. But its not clear how to do this in Iphone/IPad as when I sign in using my work email it directs me to the online icloud site and when I try to remove the email address I get the same message about changing it on the device. How do I change email address?

Most importantly I need to remove it as some sites use my work email address via apple to send validation message and I won't have access to my work email in a few weeks.

Also my Itunes account!