After market carb and throttle cable issues

[Datanutz]

Hello everyone,
I'm brand new to the forum. I rode dirt bikes for years as a teenager and just got back into it at 50. I purchased an Apollo rfz x18 125cc and a Tao Tao 110cc semi-auto 14 for my 14 year old daughter because the x18 was a bit to tall for her. I just bought the Tao Tao on facebook for $500. It's a 2019 that was ridden 7 times. It still has the hair's on the nobbie tires. Unfortunately, it sat for several months and the factory carb was gummed up so it barely ran. I attempted to clean the jets but failed to adjust the float bowl so when it started running again, the idle was all off, and it would start slowly increasing rpm as soon as you pumped the throttle. I took the advice of all the youtubers and bought a 22mm after market carb for it. When I put it on, the throttle body was quite a bit larger than the factory one. The throttle needle and needle cap (whatever you call it) were larger and longer than the originals, so I had to use them. Unfortunately, the throttle cable draw was not long enough for the new needle and cap, so when I wrestled the throttle spring into the carborator cap, and assembled everything, my throttle only had a 3/4 to 1" range of movement. So when i started the bike it immediately started revving. After attempting to adjust the cable, nothing but trying to use a dremel tool to carefully cut off the sheathing would solve the problem. Once I attempted this however, i managed to fray a few of the cable strands which then bound up in the sheathing, rendering the cable useless.

So my question now is, what size cable can I buy to fit my 22mm carb that will have enough draw to accommodate the deeper throttle body? Every comment on amazon suggests that the available cables will not fit and I will be in the same boat I am right now. How do I ask the question so google or amazon will give me the correct results. I've had this bike for almost a week and I can't even ride the thing.