WWW::Mechanize's field() function calls HTML::Form's value() function which croaks when the field doesn't exist. Without changing WWW::Mechanize (HTML::Form has a find_field function), you can always wrap your call in eval:

eval{
    $agent->field('field_name', 'foo')
};
if($@){
   if($@ =~ /No such field/i){
      print "Field missing: field_name\n";
   }else{
      print "Something else is wrong\n";
   }
}
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