Some controllers do not need the hall effect sensors, I am told. They only need the 3 wires (phases) to the motor.
IMHO, you probably don't need to connect the hall effect sensors from the motor, just the 3 phases. The other wires can be taped up out of the way, maybe in a small plastic bag, but protected from UV light!!
Basically, there are three types of motor, 3 phase NO hall effect sensors, 3 phases AND hall effect sensors, brushed DC motors, of which I do not know if they also use hall effect sensors or not!
I am going to ignore the brushed motors, as these would have two main wires, probably red and black!
The electrical difference between a 3 phase ( 3 wire) motor with hall effect and without is basically nothing, as ONLY the bike electronics will or will not NEED the hall effect sensors, the motor does not care either way!!
The 3 main fields are there and for the same wattage and voltage motor, will probably be just about identical! Any differences will be physical, a smaller or lager wire diameter.
If I understood you correctly, your original motor has only 3 wires. So simply ignore the hall effect wires. But do not cut them off as if you ever need a new controller in the future, they may be required....
IMO I think that provided you picked the right voltage and watts, one the same as your defective motor, it will work on your bike....
Do remember, if the wheel goes in the wrong direction at first, do not despair, its simple, you SWAP ONLY 2 WIRES WITH EACH OTHER of the 3.
Leave one connected where it is!! That way you will reverse the direction of the motor.
I still do not consider myself an expert on e-bike motors, as both my e-bikes had the 3 phase motors and the H.E. sensors, but I have actually worked with such 3 phase motors since 1986 on large computer printers, also with hall effect sensors.
During my time in the RN, I worked on normal 3 phase motors and had a full training as well as many years experience. Basically they are the same as e-bike motors!!! But usually much larger!!
I hope this helps you further.
regards
Andy