Upvote:4
SA Airlink can check baggage through to Dubai on Emirates. This of course means that it would be able to be checked all the way through to Pakistan as well. Just make sure when you check in at the Airlink counter that you inform the agent that you are connecting to an Emirates flight and provide them with your onward connection details.
You can pick up a boarding pass at a transfer desk, if they don't give you one in Swaziland.