JMHO, but I would think that cleaning the pump down like that
would add to the idea that pumping is a "dirty" activity and that
it contaminates the surrounding area.  Using a toilet seat is far
more risky than using your own setup on a pump that has just been
used!  I have never seen a place clean down a toilet seat between
uses (although some do...).  If it is that big of a deal, put a
clean chux over the pump, or even a large box over it (perhaps a
printer box, one of the clear things that has ventilation holes
in it...).  Pumping is not a dirty activity and it does not
contaminate the surrounding room or furnishings.  I would wonder
how employers that set up lactation rooms handle this, I know of
a few that have lactinas in them and each mom has to have her own
setup for it that she keeps and cares for on her own.  I haven't
asked, but I doubt that the moms scrub the pumps down after a
use.  I wonder at the thought that some employer would have after
seeing all of the trouble that it would take to clean down the
pump after each usage and how much of a bother it is and how much
time it takes and the thought that it must be a dirty activity...

Just a few thoughts.