First choose the fields you are interested in:

my %fields_to_show = map { $_ => 1 } qw/field1 field2 field3/;
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now modify your loop to skip fields you don't want:

foreach my $f (@{ $self->{Field_Order} }) {
    next unless exists $fields_to_show{$f};
    
    my $val = (defined $self->{Form}{$f} ? $self->{Form}{$f} : '');
    $self->success_page_field( 
        $self->escape_html($f), 
        $self->escape_html($val) 
    );
}
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