Once one has the profile there are two ways to cut out the design:
draw a profile of the ball-nose tool (note that you will need to source one with a length suited to making the entire cut) and then measure a suitable number of perimeters and assign No Offset Contour toolpaths to circles of the requisite width and at the needed depth — for an example of that approach of modeling see:
export half of the profile as an SVG and rotate it to make a 3D model, then import the 3D model into Carbide Create
Another thought…
This is a design to cut it like a lathe with a 2.25 x 2.5 cylinder blank.
Insert a 1/4" shank into the blank.
Careful!! Even at the slowest speed (Mine is 8000 RPM) it will need to be very close to balanced to start with. I would bore the 1/4" hole (slightly undersized for a press fit) on the machine.
I was talking about cutting it on my HDM, but setting it up like a lathe.
Chuck the part using a 1/4" shaft in the spindle
Use a vise to hold a turning tool
I did this for the sanding disks I made for the Mr. Fixit contest