You can use a current divider. Connect the load through two shunt resistors in parallel. The current divides between them according to their resistances: I1 / I2 = R2 / R1 (where I1 is the current through R1, etc.). Or out of the total, I1 = I * R2 / (R1 + R2). Wire the sensor in series with one of the resistors. (Note that sensor and wiring resistance must be summed with the resistor to get the true result.)
The tricky part is, wiring and contact resistances will all affect the result, at least unless you use relatively large shunt resistors (~mΩ?). Note also that wire has a strong tempco, so the balance will also drift as temperature changes. The tradeoff is how much power you can afford to dissipate in the resistors, versus how good of a match you need.
Tim