What I cannot get my mind around is how to parse through the hash and hash references, then use a regex to strip the spaces from the keys, and result in a hash with XML valid keys.

The hash looks something like:
$global{'title'}='Report for today'
$global{'data 1'}{title}='My data 1 title'
$global{'data 1'}{data}= (ref to hash)
$global{'data 1'}{footer}='My footer'
$global{'data 2'}{title}='My data 2 title'
$global{'data 2'}{subtitle}='Data 2 subtitle'
$global{'data 2'}{data}= (ref to hash)
$global{'data 2'}{'data percentages'}= (ref to hash)
$global{'data 2'}{'data raw'}= (ref to hash)
$global{'data 2'}{footer}='Footer for data 2'
and so on..
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Once I have printed the XML file, I am done with the data so changing the keys at this point will not impact any other processes. Here is what I have come up with at this point (but it does not seem to be affecting the hash references)

sub hash_remove_key_space
{    my $in_hash = shift;
    my %work_hash = %$in_hash;
    my %output_hash;    
    foreach my $ckey(keys %work_hash){
        my $value;
        if (ref($work_hash{$ckey}) eq "HASH") 
            {
            $value = hash_remove_key_space($work_hash{$ckey});
            }
        else    {
            $value = $work_hash{$ckey};
            }
        my $temp = $ckey;
        $temp =~ s|\s||isg;
        $output_hash{$temp} = $value;
        }                
    return \%output_hash;        
}

corrected code - per Sam
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