This stand is shaped to conform to the speaker cone.  Now you can wet the paper and apply a weight that stays in place until the paper dries.
Once the majority of the warpage in the cone is corrected, time to piece the tears on the cone together.  Here I have discovered a way to make that much easier and more precise.  When you have access to both sides of the cone, you can use plain Scotch tape to hold the pieces in perfect alignment.  As it turns out, this tape is very, very easy to remove later in the process.
You will need a round base plate to clamp the rim of the cone for the next steps.
It can be of anything rigid and flat.  I found that the cheapest item in my storage shed was a scrap piece of 1/2" thick sheet rock.  I cut a doughnut form so that  you can get your fingers up inside to apply pressure if necessary during your work.  Just to make sure there would be no sticking problems I covered the surface with packing tape.
Before clamping down the paper flange, I placed a sheet of poly film in between thinking that it would be easier to peel off should something want to stick.