1) Don't put any fax numbers in the field.
2) Add a non-digit string in front of the fax number (like "F: " or "FAX")
so that Outlook doesn't recognize the number as a fax number.  Faxes are
addresses as far as Outlook is concerned and that's why they appear in the
dialogue.  If you use Outlook's integration with fax software, this
workaround will break that function.

The standard behavior for the Outlook Address book is to display all
electronic addresses (both fax and e-mail). That behavior cannot be changed.
The only way to prevent the display of fax numbers is to store them in a
different field or to disguise them (e.g., precede them with an alpha
character) so that Outlook won't recognize them as phone numbers.
There are also a number of utilities available that can do this for you
automatically. Some are listed here:
http://www.slipstick.com/contacts/nofax.htm