Can I get the S21 parameter from a one-port open, short and load reading?
Your device under test has four complex unknowns, S11, S22, S21, S12.

You have three complex knowns with which to terminate the far end, short, open and match.

Four unknowns, three equations, no, it cannot be done without further information or further measurements.

Where can you get extra information from?

a) Is the waveguide reversible? Can you remove it from the system and connect the second port to the analyser, and terminate the first port. Six measurements, four unknowns. You can now find all the unknowns, if you can assume that S11 and S22 stay constant as you disconnect and reconnect, so keep those mating surfaces clean and undamaged. The extra two equations will get you an estimate of your measurement errors as well.

b) Can you assume S11=S22, or S12=S21? That would reduce the number of unknowns, assuming either gets you to the right number of equations. If you assume both, you'll get an estimate of your errors as well.

c) Do you have another section of identical waveguide, which can be cascaded with the first? This offsets the loads, to give you more equations, making the assumption that they're identical. Swap them over if you can, the extra equations will let you test that assumption.