Your idea of "auto-redirect"ing a filehandle to a subroutine is possible using a tie'd filehandle (see Tying FileHandles). This is not a sane solution for a long-term approach, but for the short term it will work:

package GreppedFileHandle;
use strict;

sub TIEHANDLE {
    local *FH;
    open my $self, \*FH;
    bless $self, shift
}

sub PRINT {
    my $self = shift;

    my $output = "@_";

    if( $output =~ /\Q$::GREP_STR\E/ ) {
        print( STDOUT $output );
    } else {
        print "Swallowed a line\n";
    };
}

package main;
our $GREP_STR = '123'; # needs to be 'our', not 'my'

tie *grep_fh, 'GreppedFileHandle';

print STDOUT "Header - always print this\n";
print grep_fh "My line with 123\n";    ## printed at the terminal
print grep_fh "My line with 456\n";    ## not printed
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For the long term approach, you should look at a logger framework (like Log::Log4perl) or a "simple" logging subroutine like your &myprint() to centralize the logging.