Non Normal Landing distances
From my FCOM performance section the landing distance required for an all flaps up landing at max landing weight of 129,200 lbs is just a hair over 4000 feet. This assumes a VREF of VREF40+55 knots, Sea Level and max manual braking and max reverse thrust. This would probably result in the fuse plugs melting after landing so if you had extra runway available and stopping was assured I would probably ease up on the braking effort and trade runway length off against braking required to safely stop. There is little to be gained by screeching to a stop in 4000 feet of a 10,000 foot runway and melting the fuse plugs.
If you are considering an all flaps up landing on a runway shorter than that IHMO you had better be on fire too.
I would have a hard time justifying a normal flap 40 Autobrake 3 landing on a runway that short. In fact the landing distance required in this config on a dry runway is 4600 feet.
There are very few airports that we operate B737s into with runways this short. In fact most airport's shortest runway is double this length.