If this external person also uses Outlook, the approach I'd take would be to
create a new PST (File>New>Outlook Data File), then copy the public folder
Calendar to that PST, and send that PST to the external person by whatever
way is expedient.  It can be mailed, for example, but you'd have to close it
in Outlook first, stop and restart Outlook, zip it (or change its file type
to something other than ".pst") and then send it.  The recipient can extract
it from the zip archive or rename its extension back to ".pst", then open it
in their Outlook with File>Open>Outlook Data File.  If you both use the same
Outlook version, you both use different versions but both are Outlook 2002
or earlier or Outlook 2003 or later,  or your recipient uses a later
version, there should be no issues.  If you use Outlook 2007 or 2003 and
your recipient uses an earlier version, then you'd have to make sure the PST
you create is a 97-2002 PST.