I've been mulling this one for a while and now 'er indoors has decided
that we need to move on it(!)

Our stairs are a bit unusual in that they are hardwood and obviously
designed to be a 'feature' of the open plan design of the house. As
with any other feature, this comes with a penalty: In this case that
the hardwood has been damaged over time (mostly by a previous owner
hammering things into the sides etc), but also that the bare treads
are pretty noisy, so were carpeted before we bought the place.

Now the carpet has worn, particularly at the edge of each tread, and
one reason for this is that these are cut square, unlike the curved
'nose' that is normal in carpeted stairs. So I have a number of
options, including taking the carpet off and leaving them bare (and
noisy) or, preferred by SWMBO, replacing the carpet. There seems
little point in replacing the carpet on a square edge, as it'll only
wear again, but how can I put a bit of a curve there?
I could run a router across but this won't make it to each end as the
string (and the wall on one side) will mean this stops before the ends
(taking the treads out would pretty much involve demolishing the
house, so no mileage there).
I guess a small radius would solve most of the wear problem without
causing enormous stretch problems with the carpet but is there
something else I can use, other than a router, that would allow me to
form a radius all the way to the edge? A hand-tool based approach
would seem unlikely, simply in terms of getting a good regular finish,
and I'm not sure that an angle grinder, SDS drill or chain saw would
necessarily do this job, before anyone suggests them.....