If someone doesn't have a suggestion, you might try renaming the contact with something like ZZ_Contact. That way it's at the end of the list--thus offering a bit more privacy.
Share the contact with your own email. The entire vCard can be kept on your email account hidden in a folder. You can then delete it in contacts. To call that contact, go to the Mail folder and tap on the vcf. Then tap the number. You can add it back to contacts at any time.