How to shield a battery powered instrumentation with USB interface?
My advice: galvanically isolate it from the computer and USB.

While you haven't really described your problem, the fact you want a faraday cage implies you need it to be quiet, and anything connected to a computer never is.

You can isolate the digital interface quite easily.

If you are using I2C, then this is available galvanic isolated. For very low noise (in wafer probing RF testers), it has been used with a fibre connection

You will see that is isolates the serial (uart) interface to the USB (FT232). The coupler IC's are very easy to use. The only vice is they have capacitance across the barrier, and they also use UHF/Microwave RF signals. Neither are so much of an issue at your frequencies.

The TOSLINK fibre connection is great for very low noise: no metal enters the faraday shield, no cables come close, No RF is used, there is no capacitance. (and they are cheap and easy to get). 

It is easy to feed uart over toslink - just hook the modules to your FTDI usb-serial board. The only drawback, is using a two wire serial (RX/TX only), so if you need handshaking, it has to be xon/xoff

[TOSLINK is the plastic optic fibre used by common audio equipment]