pass thermocouple K type through d-sub and circuit box - what might be error?
Draw your thermocouple connection from the hot-sensing thermocouple junction, all the way to the reference junction at the pins on the sensing IC, showing the material for each wire, and the thermal environment for each junction. 

Each time you change material, you will pick up a thermocouple voltage for those two materials at that junction temperature.

This means that if you connect from TCwire through a small non-TC connector and back to TCwire, and the connector is small enough that it's at a more or less uniform temperature throughout, the two TC voltages will essentially cancel out with little error.

If on the other hand you go TCwire to copper, have a long non-TC lead, then back to TCwire, your error can could as big, or bigger than (depending on the thermocouple constant of copper to TCwire), the temperature difference between the two transitions. 

If you go to copper wires at your d-sub, and stay in copper all the way to your IC pins, your effective reference junction is your d-sub. The error will be the difference in temperature between your d-sub, and the point at which the IC senses the local temperature. Depending on where these are located, local heat production could mean tens of degrees C difference between them. You could go some way to mitigating this error by putting a thermistor in the d-sub to monitor its local temperature. As most TC ICs can read out their local assumed reference junction temperature, this would allow you to correct for most of the error. Whether this increase in complexity and decrease in accuracy is worth the saving in connector cost is up to you.