Best plan is to use the machine torch (since you are building a cnc machine) and interface safely and properly using the rear panel CPC receptacle......which can easily be added to your machine if it is not on your unit. The machine torch is easier to mount (you will save money building/designing the torch mount), is easier to square to the plate (better cut edge angularity due to this), and makes for easier cable management.
I understand the need to save money....but when it comes to better performance and safety....over time th machine torch is well worth the added cost.
To interface the start signal on the hand torch....you can look at the wiring diagrams in your Hypertherm operators manual. The torch start trigger connections are easy to locate, the trigger switch is a simple on/off switch, voltage levels are under 15 volts DC on that circuit.