I'm a "no cut" kegger. My dip tubes go all the way to the bottom. It works out fine for me, since I let the beer sit a few days (I'm also a no-shaker) and the yeast falls to the bottom. I dump out the first 3 ounces, and then I'm all set. When my keg is empty, all that is left is a tiny bit of yeast sludge on the bottom of the keg, and none by the bottom of the diptube.
If you want to cut, try no more than 1/4" initially. That should be enough to get above the yeast.