The easiest way is to use the tools that CPAN provides you with...

use Data::Visitor::Callback;

my $visitor = Data::Visitor::Callback->new(
    hash => sub {
        my $new = {};
        while ( my ( $key, val ) = each %{ $_ } ) {
            $key =~ s/\s+//g;
            $new->{ $key } = $val;
        }
        return $new;
    },
);

my $without_spaces = $visitor->visit( \%global );
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