Avid Shorty 4s should be fine with drop bars - after all, plenty of cyclo-cross riders use Avid's Shorty range.
If you're going to go for v-brakes with drop bars, you need the short-arm versions such as Tektro 926AL or Genetic Mini V. These have braking arms around 1.5cm shorter than standard v-brakes, reducing the cable pull required, so they don't need pull adjust cams.