Cutter may be curved, but, the strip is thicker in the center, anyhow,
and the shear still cuts straight down.
thickness, softening the edge, is what the tapering by hand does..
and the plastic hardens over time , so don't get too comfortable..

I just use Schwalbe marathon plus tires now, myself,
[LBS still sells the tuffy strips]
the same sort of material goes under the tread,
outside the tire casing so that internal abrasion problem is gone.

Use plenty of Talcum powder.