And look at LittleMachineShop dot Com. Many of their chucks have a "compatibility" tab. You can see which chucks go with which lathes within those tabs.
As noted by others, larger chucks often take up more of your distance in the 20 inch direction, on your 9 by 20 lathe. And yes, as you open your jaws, you must be more aware of whether you have clearance with the rest of the lathe (saddle/ways).
Most of these smaller lathes are at a bigger risk of running out of power (to make an ideal cut), before you run out of physical space. A 5 inch O.D., which is cut at the ideal feed and speed, takes more power than a 3 inch O.D. You can overcome this by going with hand-ground tools, as versus Carbide Inserts.