It's probably better to fit the throttle on the left side. many of the thumb-throttles are ambidextrous, like this one that has the switch:
If you want to go for that one, you can leave off the wire that operates the battery display.
A right half throttle would probably be OK, but it's not clear whether you have enough room for a thumb throttle or whether a half-twist one has enough clearance for the brake.
As I said, any throttle will work. There are loads to choose from on Ebay, Amazon and Aliexpress. If it doesn't have a switch, you can wire in a separate switch.
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Choose whatever you want, then post here before ordering so that we can confirm that it'll be OK and how to wire it. Basically, cut the wire four to six inches from both the old and throttles, strip back the insulation and solder five wires together. Insulate with heat-shrink sleeve.