I agree with larsb that your throttle need a proper 5vdc supply voltage.
Your display is a programmable model with the 4.6vdc wires being the TX and RX communication wires. As you've found, unsuitable for the throttle's supply.
Now I've seen mods made on this type of display where the new throttle cable is taken directly into the display's housing.
With the finger throttle removed, and the new throttle's wiring taking its place. Just hook the 3 wires up accordingly with the diagram below... (I.E. the display has a 5vdc supply internally) You could also splice your key switch in at the same time, in series with the 48 wire.
If you think that you can do without any of the features that the display provides. Remove the display and install your key switch between the 48 and ---> wires. (BROWN and YELLOW)
You'll have to get the 5vdc from the controller though... either internally at a 5 or 4.3vdc pad. Or externally at the motor's hall sensor supply. The RED and BLACK wires.
You may also have to short the receive wire (RX) to ground. I speculate that this display is much like a KT controller's display...
If you're
really determined to get it working NOW. Put 3-1.5vdc batteries together in series for 4.5vdc. Connect the throttle's RED wire to batteries + , GREEN to displays connector .8 (looks RED), and the BLACK to display connector ground. (yes, both grounds need to be connected...) And tape the battery pack somewhere to give it a try. (you need to see .8vdc at closed throttle to ~3.6vdc WOT at the .8 connector wire.)
For more in depth details on hall sensor throttles and how they work, see this thread...
Guide to Hall Sensor Throttle operation, testing, and modification.
Hopefully I've made myself clear. But if any questions, please ask BEFORE wiring...
Regards,
T.C.