I'm going to have to go with the camp that states that you can choose which weapon to use.
If you have 2 of the same weapons, it states that "all attacks use the bonuses and penalties."
-ie, must use
For using a ccw and special weapons is says that attacks "benefit from the specials bonuses." (no use or penalties mentioned).
That makes it sound like if the rules aren't a benefit for you, you're not forced to use that weapon. Striking last is a penalty, so you could use the benefit of striking at init of the normal weapon.