This is (one of) my puller(s):



It's the old version Park, but the important bit is up at the hole end.
It's a flanged sheet-matal screw held on with a badly-fitting wingnut, that has had the flange squared to fit inside the square hole in a crankarm.
That goes in the end of the axle, and the puller pushes on it, not directly on the axle.
This makes sure hat the nose of the puller does not hit the edges of the crank - and the extra degree of freedom in the torque chain makes the nose less likely to gall.