open ( SCRIPT, "| /usr/local/bin/my_program" ) or die $!;

foreach ( </my/file/dir/*> ) {
    if ( /\.gz$/ ) {
        open ( FILE, "/usr/bin/zcat $_ |" ) or die $!;
    } else {
        open ( FILE, "< $_" ) or die $!;
    }
    while ( <FILE> ) { print SCRIPT; }
    close( FILE );
}
close( SCRIPT );