The hand throttle is only a driver’s aid to assist the cold engine in very cold conditions by raising the idle speed slightly. I have used mine a little after coming off choke. If you have your idle down to the usual recommended of 450/500rpm, you may find that it stalls as soon as it comes off choke. (I run my idle at 650ish as it is a smoother rise in revs for starting from rest.) Actually, if you get the tune right to idle at the 400 or so, they sound great and it impresses admirers at displays.
Even though the water jacket is up to temperature, the rest of the engine is far from it. The suction through the carbs makes the fuel atomisation situation worse as the negative pressure drops the incoming air temperature further, and carburettors can ice up. These old engines were quite cranky when woken up in the cold, and idling often resulted in stalling until the operating temperature was reached. If us oldies can remember the good-old-days of fifty or sixty or so years ago, our neighbours often ran their cars for a few minutes in the garage or driveway until off the choke because of lumpy running. ‘Blipping’ the throttle was also another skill used to keep them from stalling at idle at the lights, and not to advise you were a petrol-head
The hand throttle is also a simple aid if you need to run the engine at higher idle when you are fiddling around with tune.
The inner cable needs to be a high tensile strand (= piano wire), not a braided cable, as it has to positively push the bell crank on the carburettor back to neutral. The inside of the throttle control is interesting and a bit special too, and I can post a photo of a dismantled one if anyone is wanting this detail.