Multiplexing analog signals
Analog Mulitplexors, such as MC4051 available from several fab houses,
will do just fine. There are quad 2:1, dual 4:1, etc in 14/16 pin packages.
The random thermal noise in a 100 Hertz bandwidth, with 1,000 ohm channel resistance, will be 4nanoVolt * sqrt(100 H) = 40 nanoVolts.
Any 1/F noise may be higher, since these muxes are not designed to minimize that crystal_defect behavior.
By operating at +- 5 volts (that is, use a -5v on the VEE? and +5volt on the VDD?), your switch will easily handle 0.9 volts of DC.
You need to use a Ground plane, and have substantial R+C filtering on the several power rails. You also need R+C filtering on the Channel Select inputs, to exclude MCU trash ( 0.5 volt or so, from internal switching as the program continues to execute).
To protect against ESD, EMI, RFI, I would insert a low_pass_filter in each input from your sensors: 1Kohm resistor and 0.1uF capacitor (non-polarized ceramic, using the GROUND plane (you are using one, right) as the Return side of the energy_shunting 0.1uF.
For confidence, you might examine the instruction manual (repair manual) of commercial equipment, and learn how they protect the inputs.