Without knowing exactly how the pump "self vents" it is difficult to know if a standard pump would work, though I suspect it would. All you might need to do is when changing the water container, unplug the pump from the caravan, and drop the disconnected pump into the container to allow the water to remove any air locks in the pump before reconnecting it to the caravan.
My suspicion is the self venting pump, has a small vent hole in the extra section that allows any trapped air in the pump to escape as the water rises through the pump. Either their is some sort of float valve that closes the vent when water has reached the top of the pump, or the flow through the vent is so small it passes air easily but its much more of a restriction to water and it barely detracts from the pumps ability pressure rise the water in the pipe.