Do you really want to use strings as file handles? Why? The following works under any Perl since 5.6.0:

open my $fh, '<', $filename
    or die "Couldn't open '$filename': $!";
push @filehandles, $fh;
[download]

If you don't want to use lexical filehandles but keep on using bareword filehandles (which is what "string filehandles" are), then you'll have to switch off strict, because that's one thing that it forbids, and for good reason IMO.