How to make a power supply cable for a 10.5V 4.3A laptop OR how much higher voltage can I use
I'm a bit confused about exactly what you did. A coaxial cable generally has a conductor down the center encased in some sort of insulator with a metal braid wrapped around that. What is the 'extra' thing you cut off it?

Any way the sort of cable you use isn't that important. You're not trying to send data signals or anything. The voltage and current you're using is too low to really need anything special. So long as you're not using super fine wires it should be okay. A power cable with wires 2mm thick can handle over 7A.

The power delivery device is going to be your problem. If you need over 10V at 4.3A then a 9V at 3A supply is not going to work. It will either overheat and explode or it will detect that you're trying to draw too much current and it will switch itself off.