I'm not the expert and I'm sure that others more experienced than me will add their views, but this is how I would do it.....
Cut a strip of plain paper just a bit longer than the reed block and wedge-shaped - the width of the long reed plate at one end, tapering to the width of the shortest reed plate at the other end. Lay the strip over the reed plates so that it covers the reed tongues and valves, and carefully secure it flat and taut with masking tape (or similar which can be removed easily and does not leave a sticky residue). Ensure that the sticky tape does not come into contact with the reed tongues or valves.
The paper strip should be sufficient to prevent that bank of reeds from sounding whilst you tune the uncovered side of the reed block. Once you've done one side, repeat the process for the other side.