If you are using the Web API you can use the headers parameter as you mention. If sending via SMTP you can just add the headers to your message.
There are a few headers defined in RFC 4021 that support this as well as some custom ones. I'd use the following JSON for the headers parameter to start:
{“Priority”: “Urgent”, “Importance”: “high”}
If that doesn't work you can also look into the X-Priority
and X-MSMail-Priority
headers.