Technique or tool to properly expose LED strip wires?
I have used weatherproof LED strips like in the picture below.  My technique was:


Cut the strip to length at one of the designated places with sharp scissors.
Using a not-to-sharp knife ( I used my pocket knife rather than a razor blade ), cut through the rubber coating perpendicular to the strip.  Cutting into the wires or plastic backing strip shouldn't be an issue with an old knife, but still be careful.  if soldering, you only need to cut back enough rubber to clear off the contacts.  If using the crimp connectors, use a connector to measure where the rubber should be stripped (about 1/2" back).
Bend the strip along the cut that you made.  You should only have to bend it about 90 degrees.  This will make the cut open up.  If you didn't cut all the way through the rubber, that will be obvious now, and it should be easier to cut the remaining material.
Using your fingernail or your old knife blade, try to get under the rubber layer and start peeling it off.  On my strips, once I was able to get it started, the whole chunk would peel cleanly off.
If the rubber shreds or does not come off, use the knife to continue peeling any residue off.  If necessary, lay the strip on a hard surface and use the knife to scrape residue by holding the knife blade perpendicular to the strip.  If you angle the knife, there is a greater chance of cutting the strip.




image taken from: http://www.usledsupply.com/shop/z-how-to-RGB-strip-wire-solder 

I have not used their how-to, I have only used the non-solder connectors.  I was able to make my splices look much cleaner, but I couldn't find a better image.