I would like to upgrade our servers OS from Wheezy to Debian Stretch which does not have CGI.pm in the Perl core. I believe the upgrade to Stretch will leave CGI.pm intact (which the scripts need), but if not, what do I do?

Debian Stretch should have a package containing CGI.pm. https://packages.debian.org/search?searchon=contents&keywords=%2FCGI.pm&mode=path&suite=stable&arch=any lists several packages containing a file named CGI.pm. libcgi-pm-perl seems to be the right one.

apt-get install libcgi-pm-perl
[download]

... and you have CGI.pm back, unfortunately the 4.x series that lacks proper upgrade information. Read the change log (/usr/share/doc/libcgi-pm-perl/changelog.Debian.gz and /usr/share/doc/libcgi-pm-perl/changelog.gz after package installation) in addition to the documentation. "CGI::param called in list context" confusion also contains useful information.

Alexander