Switching thermocouple signals using an analogic Mux???

Hello all.

The voltage signal of a thermocouple type T is aproximately 40uV \ °C for a temperature range of 0 to 100 °C. 

I want to read 15 type T thermocouples, all of them have same reference (ground reference, negative wire, minus wire).

I want to use an analog muliplexer (16:1 mux, model 74hc4067, it will be powered from a +3.3V rail) to switch the positive wire (positive voltage signal) of these 15 thermocouples into an OPAMP (I am going to use the LTC2050 from Linear Tecnology, it has a maximum input offset voltage of +- 3uV and very low offset drift generated by temperature variations).

I know the analog switches of an analog multipler have an internal resistance when conducing, but I think there is no problem because the non-inverting input of OPAMP has very high impedance.

I will use a non-inverting amplifier with a gain of around 200x, and its output will be connected to a 18 bit precision ADC with internal precision voltage reference and I2C interface to communicate with a microcontroller.

The main doubt now is:

Is it possible to conduce very a small voltage signal through an analog switch????
Because the type T thermocouples generate a voltage of around 40uV / °C.
Somebody know if a there is a minimum acceptable voltage level in order the analog switch can conduce the signals???????