Hi Crispin, when you send an email in Outlook, the sender field is a dropdown list. One option is to select "other email address". Just enter the external domain email address you want to send from, and Outlook will remember it. The next time you want to send from this email address, it will be available in the dropdown.
My wife uses Outllook 365. I set up four separate Outlook inboxes for her @iCloud email address plus her three external domain addresses. When she replies to an email in an external domain inbox, the sender field shows her @iCloud email address. All she has to do is pick the correct external domain email address from the dropdown list before sending.
If you don't want to set up separate Outlook inboxes for all your iCloud email accounts, all emails should show up in the @iCloud.com account that was used to configure the external domain email.
Ernst