I take it you are getting those IP addresses from your ISP, which means your ISP is responsible for the routing. If this is not the case, then the following will not hold true.
However, is your switch managed or unmanaged? If managed, you should be able to setup the LAN IP subnet so the switch knows it does not need to forward packets destined for the LAN.
If your switch is unmanaged, then you are stuck. Your ISP can configure to not deal with packets destined for the local subnet you have.
Which brings up another question. Are you sure your ISP is giving you a full Class C? If the subnets do not match what the ISP is routing, then this could cause packets originating from the LAN not to be sent back to the LAN.