Bobwills,
The picture of your alternator seems to indicate that's it's internally regulated. If so, you do'nt need to remove the regulator. Just bypass it.
See that little D shaped hole in the back of the casing just to the left of that 2 wire connector ? Have a look inside that hole, with a light if need be. You should see a small metal spade lug, just like the ones that your above-mentioned connector plugs into.
Those three lugs are part and parcel of the regulator and the one behind the D shaped hole is to test the alternator output. If you short it to ground, (the alternator case) with a screwdriver, you effectively bypass the regulator and maximum output is produced.
The alternator output would then be varied by the voltage applied to one of the other two lugs under the connector.
Cheers,
rivets
The diagram posted by Blasphemy000 above is correct.
So if you have an internal regulator and you disable/bypass it as above, and you hook everything up as per the diagram, it should work fine.