Plug/socket between thermocouple wires and the amplifier
I do not know the accuracy that you will require in your temperature measurements.   

Your idea of using copper wire and connector sockets is reasonably ok as long as you are aware of the following :  

Where you make a connection from thermocouple wire to copper, that creates another thermocouple in itself. This isn't a great problem since the temperature of the "undesired" thermocouple is likely to be at room temperature (constant?)  

No matter what you do, you always end up with undesired thermocouples (example when you connect your thermocouple directly to your circuit board copper, darn it.)   

Thermocouple Selection and use is a page you can go to for more information.  Especially the Cold junction compensation (CJC) section.  

EDIT added : You should twist your extention leads together to reduce electrical noise from the environment. Twist each pair, do not twist the bundle all together.