In my opinion, if you know you will have a very small amount of time to try the new instrument before you will have a performance, try to select some easy organ pieces. Pick up pieces that you can play very well, not too hard pedal part etc.
Also, you should try to find out as much information about the organ as possible before going to an actual instrument. If you contact the local organist, she will provide you with an organ specification and might tell you specific things about particular instrument.
At the beginning when you will try a new instrument do not play fast. Start from the principal 8' and listen to the acoustics, later add more stops until you reach Organ Pleno registration (principal chorus with mixtures).
It's hard to adjust to a new instrument, but at the same time it is the thing that makes organ the most exciting instrument in the world. You never know what you will find and how the things will go.
This is a true beauty of being an organist.