If CGI implements ->can, you should be able to get to a code reference that does what you want:

my $old_method;
BEGIN {
    $old_method = CGI->can('header');
};
sub CGI::header {
    print "Before\n";
    $old_method->(@_);
    print "After\n";
};
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Otherwise, I wouldn't mess around with CGI and its namespace but implement a thin class that just delegates to CGI:

package MyFakeCGI;
use CGI;
sub new {
    my ($class,%options) = @_;
    $options{ cgi } ||= CGI->new;
    my $self = \%options;
    bless $self => $class;
};

sub header {
    my $self = shift;
    print "Before\n";
    $_[0]->{cgi}->header->(@_);
    print "After\n";
};

# Delegate everything else to CGI
sub AUTOLOAD {
    goto &CGI::AUTOLOAD;
};

# Don't delegate DESTROY
sub DESTROY {};

1;
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You don't have to stash a reference to a sub in order to call it. I don't really know what you are trying to do. Please provide a minimal example showing what you tried similar to the following code and tell us what doesn't work

use strict;
use warnings;

use CGI qw/:standard/;

sub header {
    return "this is not the header you are looking for\n";
}

print header;

print CGI::header;
print main::header;
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