First, correct - private IP addresses are not routable over the Internet. You will need to configure address translation or port forwarding on your router.
Second, what are you actually targeting? If you haven't already configured the address translation or port forwarding above then nothing will actually be visible on your client machine to the Internet. There may be some administration/management ports open on your router but that will probably be it.
Finally, if it's your own private network and you don't have any public services running, then you may as well just test your machine over the local network.