I use the Butel Software and it works with both the 8200 and 8600. In fact, when you start the program, it says it supports both models.
The cable you use for the 8600 is needed to program the 8200 because the cable that attaches to the 8200 has a DB9 plug at the other end that is the same female DB9 that is built into the 8600.
There are two versions of the 8200 cables. Both are called "AOR CC8200" but depending on the serial number of your receiver, you have to have the correct version. Only the very latest releases of the 8200 used a version that has a much smaller plug on the end that goes into the lower right side of the 8200.
Which AR8200 do you have? AR8200Mk2 or AR8200Mk3. If it is a AR8200Mk3, what is the serial number or post a picture of the plug on the right side that is just below the power plug.
UPDATE: I see in an earlier post, you said you have a AR8200Mk2 version, it uses the original "fat" plug version of the CC8200 programming cable. I will in a little while post a picture of the two versions of the cable.