Radio buttons are no different than any other form field (dropdown selection box, text input, hidden input, etc.). So, if there are reasons to sanitize the others, then yes, the same would apply to radio buttons.
"Vulnerable to security threats" is such a broad, nebulous phrase that one could easily say yes, of course it is vulnerable. Are you sending the e-mails as HTML or plain text? If the former, someone could inject their own HTML code into the message, for example, if you weren't sanitizing it at all.