If it's actually a .62" then I would use a .58" or smaller ball. Anything bigger will cause problems once some fouling starts to build. Measure your bore with some calipers before you pick a ball size.
Lee makes a double cavity .575" mold that would be a good inexpensive choice. Another option is ballmoulds.com, he makes decent custom ball molds from brass.
My two 69 caliber guns are .685" at the muzzle and I've been using a .65" ball with decent results. Accuracy is "minute of man" at 50 yards with my 1777 musket and the An IX pistol is "minute of man" at 15 yards. I have noticed accuracy does start to drop off after 5-6 shots if you don't swab the bore.
Here is a recent 3 shot "group" I fired at 10 yards with the An IX. (first shot is low left and the other two are right next to each other). I had some trouble getting the first shot off (oil on the frizzen) so I may have pulled the first shot.
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