I can think of 3 solutions to your issue:
First, you can purchase calibrated thermocouple wires where the inhomogeneity has been calculated and reported.
Next, you can calculate the inhomogeneity of the thermocouples yourself. This is discussed in Section 9 of Euramet CG-8, "Calibration of Thermocouples":
In many cases the inhomogeneity of the thermowires is limiting the measurement uncertainty. For high precision calibration it is therefore necessary to test for inhomogeneity, using a method that involves locally changing the temperature profile along the length of the thermocouple, by heating or cooling, while maintaining the measuring and reference junctions at a constant temperature, such as 0 °C. The region of heating or cooling is slowly moved along the length of the thermocouple, whereupon local inhomogeneities can be detected from changes in output.
It is recommended to estimate the uncertainty contribution from the inhomogeneity as rectangular contribution, with a full width equivalent to the largest difference found for any two measurements during the test. If the test was only performed over a small length of the thermocouple, the largest difference in emf found in the measurement should be taken as half width of the rectangular distribution.
The third method, which may be the best for your case, is to estimate the worst case inhomogeneity effect, also in Euramet CG-8 Section 9:
In cases where no individual measurement of the inhomogeneity is possible, it is recommended to take at least 20% of the Class 2 tolerance value for the corresponding type of thermocouple according to EN IEC 60584-2 as contribution (k = 1) to the uncertainty .
Euramet CG-8 is available as a free download at:
https://www.euramet.org/Media/docs/..._cg-8__v_2.1_Calibration_of_Thermocouples.pdf
