No need to lowercase the array, just the 'work-out' hash keys, if we assume this simple approach:-

# @input assumed by statement of requirement
my %done = ();
my @output = ();
for ( @input ) {
    unless( $done{ lc( $_ ) } ) {
        push @output, $_;
        $done{ lc( $_ ) } = 1;
    }
}
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