I noticed you were opposed to loops for some reason. I have a hard time imagining a good reason for a loopless stragegy. Here is how I would begin:

sub send_values {
    my ($args) = @_;
    my $values = "Your Results are:\n";
    $values = join '',
      map { exists $args->{$_} ? $args->{$_} . "\n" : () }
      qw( name address pic id zip phone );

    # do whatever it is you want to do with $values.
}
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You would still get an undefined value warning if the caller did something silly like: send_values( { name => undef } ); ...but that seems unlikely, and probably truly deserves a warning.

If your reason for avoiding loops has to do with performance, I recommend abandoning that concern for the time being.