Indeed
You can't double up close combat weapons, as its already been stated, and the only exception in the ork army I remember is Mad Doc Grotznik, who has both a powerklaw and an urty syringe . You can use the powerklaw for the high strength no save attacks, or the syringe to wound on 4+, but in practice, I've rarely used the syringe, unless fighting opponents with low armor saves or very low initiative (basically IG or other Orks).
Always go with the powerklaw. The big choppa will only break your heart. As for the gun, I personally like the flamer/shoota combo.
Of course, the best option as I see it, is to put the warboss on a bike as well. That, or replace him with Ghazghkull, or the Mad Doc. A regular warboss on foot isn't going to do much damage. If I was simply filling an HQ spot for cheap, I'd do a big mek with SAG instead.