While if( $_file_name !~ /^(\s*)$/ ) { does handle the case of undef, it will cause a warning:

use warnings;

my $_file_name = undef;

if ($_file_name !~ /^(\s*)$/ ) {
    print "ok\n";
}

__END__

Use of uninitialized value in pattern match (m//) at test.pl line 6.
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gav^