First make sure you can connect from one internal system to the target system. If that is working, then you need to configure your router/firewall (assuming it is a NAT device) to forward port requests to the system you are trying to control. If you have more than one system you are trying to accesss from an external system, you will need to configure each VNC server on a different port so you can configure a forward to each internal system (IP).
In a nutshell, the switch is an unmanaged device and therefore doesn't block anything going through it (it is transparent). The key is to make sure the internal test works.
Clear as mud?