handles => {
   param => 'param',
},
[download]

is effectively

handles => {
   param => sub {
      my $plack_request = shift->plack_request;
      return $pack_request->param(@_);
   },
},
[download]

So instead of using around, you could use

handles => {
   param => sub {
      my $plack_request = shift->plack_request;
      return (wantarray
         ? $plack_request->param(@_)
         : $plack_request->param(@_) // ''
      );
   },
},
[download]

One less layers of subs, and less action at a distance.