Luke Meyers wrote,

  "I am wondering whether I can use a 5 ampere, 120 V.A.C. variable
  speed fan control switch on a 6 ampere 120 V.A.C.  vacuum motor for
  an electric suction source on my player piano?  Is this prohibitively
  dangerous ("Stop - Danger of Electrocution!") or more of a "take
  caution" procedure?"

Luke, you answered your question in your first sentence.  The
controller is rated for 5 amps, the motor for 6 amps.  The controller
is not heavy-duty enough.  Granted, electrical items are usually
down-rated (they can actually handle more than the stated amount),
and the motor is likely not at full load, so you will probably get away
with it, but it's not good electrical practice and I would be much more
comfortable with a 10 amp rated switch running a 6 amp rated motor.

I bought some speed controllers off an Internet electronics surplus
store a few months ago that were rated at 10 amp and I think cost me
about $4 each!  No box or anything; you have to create your own
mounting system.

I've used one, so far, on my portable testing vacuum box.  I mounted
it on a blank faceplate, drilled a hole for the knob shaft and mounted
the faceplate on a standard electrical box.  Now I can dial the supply
down to a half-inch of vacuum, or up to around 20 inches (apparently
the upper limit of this vacuum box -- which I bought off eBay, so
I have no idea as to its origin).  The controller doesn't even get
warm, nor does the motor.

This is just my opinion and I'm not an electrician, I just play one
at home! :)

David Dewey