You can use that router. Once you've setup the Slingbox for viewing locally, its the routers responsibility to allow remote viewing. I recommend that check your router's firewall rules. You'll need to make sure that that the corresponding public UDP and TCP ports and being forwarded to your Slingbox's private IP address.
Try this guide (http://portforward.com/english/routers/port_forwarding/Dlink/DIR-300/SlingBox.htm)or below articles to see if they can help you.
IP address and Port Number: http://support.slingbox.com/get/KB-005866.html
Port Forwarding: http://support.slingbox.com/get/KB-2000068.html
Network Setup Assistant: http://support.slingbox.com/get/network-assistant.html
Manual Changes: http://support.slingbox.com/get/KB-5000126.html