Thanks guys!
Lou, that model you found looks promising. It might still be a bit large, but worth a try. It is also not the one I found. The one I found is
At the time I was looking, there was a Chinese ebay seller in Australia (I'm not kidding) who supposedly sold plastic model kits of 1:160 scale Boeing 737s! I bought couple and I got burned. The model kit looked like a copy of another company's model of a Boeing 777 (not sure of scale - maybe 1:350?) packaged with a decal made for a 737 (in 1:160). I guess that this combination would yield an airplane with a length of a 1:160 737, but the shape of it was all wrong! I still have those kits (they weren't very expensive so I kept them for some future project).
EDIT: I've read somewhere (maybe in that related thread on the A-board) that there was some modeler, who is a Boeing employee, who was supposed to make correctly scaled 737 resin bodies. Not sure whatever happened to that venture.
EDIT 2: I have feeling that the scale of all these models is very approximate.
But the Flight Miniatures model I have is larger than a 1:200 Hasegawa 737 kit and smaller than the Airfix 1:144 737 kit. I'm talking about the fuselage diameter.