Zone are the best thing for this job.
Based upon what you stated about ~9.3mm, this would imply you are using 1oz copper (reversing Kicad value).
The concern is Kicad’s calculator uses IPC-2221 for this and this has been superseded by IPC-2152. Using an IPC-2152 based calculator results in a trackwith of 24.4mm (for 10C temp rise, 1oz copper)
Now some say IPC-2221 is “good enough”, IMHO it isn’t… and a doubling of the needed trackwidth is testament to this. Ill leave it up to you with regards to what width you feel is correct.
As to the layout… I agree with @paulvdh, the separation between the two shapes can be very small, the minimum etch width for this weight of copper (8thou?) because the voltage difference is going to be in uV as the associated SOIC8 part will have a resistance around 100uR
What I would do however was move the terminals as close to the part as possible as this will minimise the volume of copper conducting the current. Likewise I would utilse both sides of the PCB to spread the current across two layer - The banana plugs will provide a double-sided connection so you just need some supporting via’s around the sensor
The usual rule of thumb is a “standard 0.3mm” via with typical plating is good for ~0.5A (for a 10C temprise)… likewise x-number of such a via ~ one via of x-time the diameter … So there is a happy medium of a number of vias of a specific diameter