Would I just need to put a 50 ohm resistor in series with the output of the instrumentation amplifier?
More or less, but you should take the output impedance of the INA into account, e.g. if the output impedance is 10ohms, then you would add a 40ohm series resistor. Whether or no that matters depends on whether the interconnection is electrically "short" or "long" compared to the signal's wavelength, and that is frequency dependent.
But be careful: some spectrum analysers cannot tolerate any DC component, and many are very sensitive to too much input power. Too much of either and the unprotected front-end-mixer is instantly destroyed. Check the spec of your SA.