Cable joins on wiring LEDS in parallel
What you can do is solder the LED to the resistor with the bare wire obviously as you mentioned but cover it up with heat-shrink tubing insulation material.  This is the best way to avoid short circuit connections.  Note that it may be time consuming to actually have to do this for a meter square of LED connections.  Here is an example below of what I am talking about:



You would have to place the heat-shrinking element before you solder your LED to your resistor and when the solder connection is done, move the heat-shrink tube down over the solder joint.  Using a solder iron or a lighter, you can shrink the tubing material very easily and make it stick to the solder joint.  That way your circuit will be protected from potential short circuits and no LED will go bad.  

Be careful to not place the solder iron or the lighter over the same place for too long since it might cause the solder joint to melt and detach itself.