Please look at CGI::Application (and also CGI::Application::Dispatch, once you've digested the former). The documentation is very readable and includes examples which you will find illuminating.

I don't want to spoil the plot for you but here's a snippet - using this approach your view runmode may look like:

sub view {
  my $self = shift;
  my $q = $self->query;
  my $dbh = $self->param('dbh');
  ...
}
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C::A objects can get to the cgi object via $self->query, so no need to pass that around. And you can pass other stuff between runmodes using C::A's param method.