I have not looked at the datasheet, but I assume the sense voltage should be relatively fixed for a certain current.
One easy solution is to use a potentiometer over your shunt resistor.
If you use a 10 Ohm potentiometer, then it's 100x bigger then your 100mOhm or so shunt, and also 3 orders of magnitude smaller then the input of your IC, so it's input impedance effects are negligible.
A disadvantage of this is that the voltage over the shunt must be bigger then the sense voltage you need, but it's very simple.
Of course 2 fixed resistors also work.
Alternatively, you can use a series and/or parallel combination of standard E12 resistors for your shunt to get it to just the right value.
The most often used way is to use a low value shunt, and then amplify the voltage over it, but this would need an extra opamp, with very low offset voltage and surrounding components, possible bandwith problems, etc.
Another option is to use a smallish (10 to 100 Ohm or so) resistor between the active side of the Shunt and the IC, and then feed a fixed current through it to add a fixed offset.
If you have a relatively stable supply voltage, then a simple resistor as "current source" is probably good enough.