I'd take a bit of a different approach, and have the logging module create a default log handle internally, with a log() function that takes a message and an optional filename. If the optional filename is sent in, we create a new handle internally and log to it, otherwise we log to the default handle. Here's some code I put together very hastily as an example:

use warnings;
use strict;

package Log; {
    sub new {
        my $self = bless {}, shift;
        my $log_file = shift;
        open my $fh, '>', $log_file or die $!;
        $self->{default_log} = $fh;
        return $self;
    }
    sub log {
        my ($self, $msg, $log) = @_;

        my $log_fh;

        if (defined $log){
            # filename sent in
            open my $fh, '>>', $log or die $!;
            $log_fh = $fh;
        }
        else {
            # use the default fh
            $log_fh = $self->{default_log};
        }
        
        print $log_fh "$msg\n"; 
    }
}

package main; {
    my $log = Log->new('default.log');

    $log->log('default log message');
    $log->log('alternate log file msg', 'not-default.log');
}
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Default log file:

$ cat default.log
default log message
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Alternate log file:

$ cat non-default.log
alternate log file msg
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Is that kind of the idea you're after? Something along these lines prevents the user of the module of having to create and send in their own handles. If I'm off-base, just let us know.

update: If you want the user to be able to send in their own file handle instead of just a file name, the log() method could be changed like this:

    sub log {
        my ($self, $msg, $log) = @_;

        my $log_fh;

        if (defined $log && ref $log ne 'GLOB'){
            # filename sent in
            open my $fh, '>>', $log or die $!;
            $log_fh = $fh;
        }
        elsif (defined $log && ref $log eq 'GLOB'){
            # file handle sent in
            $log_fh = $log;
        }
        else {
            # use the default fh
            $log_fh = $self->{default_log};
        }
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...and called like this (continuing on with the main example above):

open my $fh, '>>', 'alternate.log' or die $!;

$log->log('msg', $fh);
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/update