The filter has a resistance to air flow, depending on which type you use. The size of the filter is larger to allow as much air as the smaller opening would pass.
It is possible to put a small section of duct on the side of the furnace with the 15 X 19 hole cut in one side and the 16 X 25 cut out of the other side for the filter. The duct could be only 4" thick and still allow the air to pass, of course the ends of the duct have to be capped. OR you could go to a heating or sheet metal shop and have them make you a transition for the two sizes.