In list context, when the key isn't present, the param method returns an empty list rather than undef. Put the param calls in scalar context and all will be well:

use CGI;
my $cgi = CGI->new(
    user_name => 'foobat'
);
my %data = (
    email => scalar( $cgi->param('user_email')),
    name  => scalar( $cgi->param('user_name'))
);
print "@{[keys %data]}\n";

__END__
email name
[download]

Can you save yourself some work by looping over the params list and deriving your key names by substr or substitution?