There are three types of asbestos, brown, blue and white.  Only blue
and brown asbestos are allegedly dangerous, and this only when someone
is exposed to it over a long period.  Most asbestos found today is of
the white variety and is in the form of a composite, using some form of
cement to produce a sheet.  Even blue and brown asbestos in the form
other than open fibres is not dangerous until worked, which will
release individual fibres.  The small amount in the piano pump is not
going to be of any harm, even if it were blue or brown asbestos.  As
is usually the case with these scares, you will put yourself at a
greater risk removing it than leaving well alone.  It could be said
that the only people to gain from the asbestos scare are those
involved in its removal.

Best wishes from Great Britain,  Nicholas Simons.