If you're only emailing it to people in your database, you could completely omit these fields from your form. The link to the page hosting the form will be converted to be a unique URL for that lead and by clicking through it, they'll be cookied and recognized as that lead (if they're not already).
The danger to this is if they share the link, or if someone finds the URL in a different way.
Alternatively, you can have the fields on the form and have them prefill by changing the settings in the form itself.