There is never anything wrong with writing "n/a" in any kind of form. There was a long overlap during which any form that took contact details already had fields for email address and mobile phone number, but before either of those were as ubiquitous as they are today; nobody processing those forms ever ignored one with "n/a" for email address.
Granted, it might be less prudent to skip some fields than others, of course.
Granted, it might be less prudent to skip some fields than others, of course.