so there are two ways to do this, the safe way and the dangerous way. Safe way requires unsoldering the little brass end that holds the cable in the carb slide, pulling the inside cable out of the outer sheath, cutting back the outer sheath about 1/4 inch or if you have plenty of adjustment at the throttle to make outer longer then go 5/16 cut off outer. If you are not comfortable with removing the end of the inside cable you can do it without removing it if you have a steady hand with the dremel with a fiber cut off wheel.
1) remove the shiny crimped on end on the end of the outer cable. it it is crimped on real tight use a razor and cut the outter rubber at the bottom of it and then you can try turning it and pulling it off with the rubber together.
2) the outer cable may be round wire of flat wire, my pics are flat wire, cut across one coil so that it will shorten it about 5/16ths in your case. If the inside wire is still inside the outer cable then you DO NOT want to go all the way thru. just grind it most of the way thru then bend the end with a pliers and the metal will fatigue and break off.
3 If the inner cable is still inside you will have to unwind the small cut off piece of the outer cable. then try to get rubber out of the shiny end piece and get it back over the outer cable. It is not easy to do so take you time. Here are some pics of what this looks like, the outer end piece, a cable then with the rubber cut off and the end of the inner cable brass piece you silver solder on to fit in the slide.