If you clean the rust from the area around the nut, you'll see that the big hole surrounding the nut is threaded. A proper flywheel puller would screw into that large hole. Then, a bolt going through the center of the puller would apply pressure to the crankshaft's end. Pulling force will be concentrated in the center of the flywheel, not around it's edges.
A puller that pulls on the edge of the flywheel could easily tweak it.
If you're like me, you're impatient and a cheapskate but have a welder.. and would carefully tack-weld a large nut onto the center of the flywheel.. then use a bolt through it to apply pressure to the crankshaft end .. after it's pulled, cut the welded bolt off.
Welding on and around a flywheel (with it's magnets that attract metal from grinding and cutting and which can be de-magnetized from high heat.. and with the delicate wires all over the place) requires some careful thought..