Tool for cutting Delta brake cable...
 

I have just a tiny bit of cable still coming out from underneath the Delta brake cover as my wire cutters were too thick, how do I get rid of that last bit? Cable fraying would not be a concern as the brakes are now properly set.

A dremel with a cut off wheel. You can probably use a set of needle nose pliers to hold the end while you cut.

When I put cables on Deltas, the very last thing I do is cut the cable. I run it through and down by the tire, get everything adjusted like I want and then cut the cable with the dremel.

+1 on the Dremel type tool, however I wouldn't suggest the cutoff wheel. Rather use the small sanding drum -it will grind down the cable in a few seconds.