To my knowledge, there have only been a few different threads used for crank pullers (and arms) with the most common one accounting for about 95% or more of all cranks. (for a while Campagnolo used a LH version of this same thread).

Odds are your problem isn't that you have the wrong puller, but that the outermost thread of the arm is damaged slightly so you can't get the puller started. take a good look at the RH cranks thread, and if you see any dings, use the tip of a half round or rat-tail file to remove part of that 1st thread (no more) at a 45 degree angle. Then, assuming both cranks are the same brand, use the puller that fit the left crank and you should be OK.