The L's internal speakers are both 16ohm, wired in parallel for a total load of 8ohms
The amp is expected to run at 8ohms, so if you only use one at a time (the amp "sees" 16ohm) you will not damage the amp. A Tube amp needs to see its rated load or higher without sustaining damage. Lower impedance will strain the output section of the amp. However if you dont use a speaker which has a matched impedance with that of the amp you will alter your sound quality - in one way or another you will change the freq. response characteristics and power output capability. in other words, it will work, but not efficiently.
Also note that the L's speakers are not identical - they are made by 2 different companies and have a different shapped cone - I am not sure about the specifics but I'd guess that each is tuned to perform better with high or low freqs. Using them separately would very well affect the sound in one way or another. Not sure if your ears would be picky about it. Maybe there is no difference at all - but why did hammond use 2 different speakers to begin with?
My 2cents are to find a new full range speaker for the Leslie. (whats wrong with the current one?)