Not counting my grandfather's buck saw, I've used frame saws, turning
saws, for over 30 years.  The smallest I have is a bit larger than
David's beautiful creation.  The largest sports an approximately 30 inch
blade.  The largest I've seen (in photos) are pit saws.  Some have some
sort of "handle," most do not.  Now, I've seen fret saws with wooden
frames, but I'm not personally familiar with using one of those -- its
use may be different.  But without exception I always grasp the frame
itself in use.  Most of mine have those split wooden pins holding the
blade.  But not all.  The largest I currently have in my shop holds a 20
inch blade held in steel pins.  Those pins terminate in eyes so that you
can stick an awl in them to adjust the angle of the blade to the frame. 
The blade is to be canted to the right, not held vertically to the
frame. I seem to remember St. Roy showing this use; you're siting down
top edge of the blade, watching the blade work into the wood you're
cutting -- often an important advantage.  Old style coopers, in cutting
the barrel heads into circular disks, set the blades at right angles to
the frames.  True of the framed pit saws, too. 

In any case, the blade is not dependent on a handle for stability of the
blade, but on the frame.  Move the frame and the blade follows.  With
such a light blade it is difficult to control the frame by using the
"handle."  However small, a frame saw is not a metal framed coping saw
or fret saw.  The handle?  It's best, perhaps only use is adjusting the
angle of the blade from end to end so that it is perfectly straight. 
The weight of the frame, in combination with the small, light blade,
will not be stable, but will want to wobble and give you grief.  Grasp
the frame in use, and that problem disappears. 

Mike in Woodland