It'll be more easy for us to give you correct solution if you'd provide some sample mock up data. However, I've tried to replicate your scenario using superstore data.
Lets assume Sales and Profit measures as your Business Impact & Risk scores, Region as Region and States as Sites.
Drag these fields on canvas like below screenshots.
Once done last important thing you need to do is
Set the marks to label Highlighted
See the below screenshot.
Let us know if this help. Else share some sample data.
Note: Scatter Plot will not be the good visualization to show all the labels in a view because your label will be overlapped in some of the cases where sites have equal scores. Better you should use bullet chart. Give a try.
This worked for me.
I'm glad that worked
Could you please mark my answer as correct so that it helps others who have similar query and this thread gets invisible from the unanswered list?