Although the small and large set of lifting knives that I make and sell are intended primarily for lifting, I find the smaller knife also useful for paring the edges of a spine that has been removed. The edges need to be pared to achieve a smooth join when it is replaced.
Some binders use a Dremel or Foredom tool, and Jim Reid-Cunningham demonstrated this at the Guild of Book Workers 2013 Standards Conference in Washington DC last week. He used a conically shaped coarse grinding stone. Some binders use a scalpel for this, though I haven’t found a blade shape that is easy for me to use.
I generally use a small lifting knife which gives me a lot of control, especially when paring a spine with raised bands intact. Notice that I am working with the knife bevel down. This raises the angle I hold the knife at considerably so that I do not have to flatten out the spine. It also allows me to quickly adjust the angle of the knife to match the curve of the leather of the bands.
Whichever method you use, likely the most important aspect is to lift the spine as smoothly, cleanly and evenly as possible in the first place.