The screen rolling tool you have should be fine to use.
Andersen window screen metal spline.
First roll in the wire on one side of the screen frame that will make an indent so you can place the spline in position.
Any suggestions as to removing carefully or replacing with a similar product.
The spline is white aluminum square stock.
I can not think of a way to remove it without twisting and or bending it too much to reuse.
This patented screen is made with micro fine stainless steel mesh that lets in over 25 more fresh air and provides 50 greater clarity than conventional andersen insect screens all while keeping out unwanted small insects.
With the screening tool place the wheel towards the outside of the spline and start rolling it in that way if you slip the wheel of the tool will jump on the outside of the screen instead on top of your new screening.