I also dive that type of wings.
If you choose, you can just leave the second inflator stowed and not attach a second LP hose. I do this in most cases, but when diving wet I will rig the second LP.
It does NOT double your buoyancy and using both would be most ill-advised. (sorry Battles2a5, but unless I misread your post I disagree ). Since both bladders are in the same shell, the total volume is going to be restricted. I would strongly advise AGAINST using both in any case beyond failure of the first, as then you'll be guessing as to which you will need to empty or fill.
But stevead is very correct in pointing out that capping off the right side inflator will render it useless. The two bladders are independant and unless you're far more flexible than I am, you'll never get it to your mouth to orally inflate it.
In this case, plan (& train) to shoot a bag for redundant buoyancy.
Hope that this helps,
Steve
PADI Course Director
TDI Deco/Adv. Nitrox