Just called godaddy, they offered me the opportunity to press # to hold in silence. What a breath of fresh air. If they can do it SO CAN WE.
Can someone figure out how?
A $50 prize to the best solution!
This sort of feature would have to happen upstream in Asterisk. The hold music app does not support dtmf actions.
Well, there’s the breakout queue option. I played with that a little but it was too clumsy.
I have set up a “Press 1 to wait, 2 to wait in silence…” also a little clumsy.
Previously, someone said there was a “jukebox” script out there somewhere.
I know it can be done…
It would make the world a better place, possibly even helping reverse global warming!
I would suggest you look at using the featuremap and applicationmap defined in the /etc/asterisk/features.conf file in Asterisk for in-call dynamic customer satisfaction 
http://www.asteriskdocs.org/en/3rd_Edition/asterisk-book-html-chunk/AdditionalConfig_id256654.html
and
the asterisk command MusicOnHold on the channel:-
https://wiki.asterisk.org/wiki/display/AST/Asterisk+11+Application_MusicOnHold
as the appropriate application.
Using # is ill-advised as ## is already taken by default.
IMHO opinion that would be the easiest, just pre-announce such capability and use your chosen digitmap to call an application that toggles it or even gives you a choice of your “genre” of MOH, the possibilities are endless but also the effort would not be worth 50 bucks of most folks time make it 500 and I would think about it 
.
simple if you are OK with not using #.
Just point to ivr saying press 1 to hold with no music .
1 would transfer to a que or ring group with no music. If nothing pressed…aka invalid or time out destination set to 3 seconds or so would point to que or ring group with hold music.
Just be sure to set your disconnect on no traffic to a long time.
How would you like to pay? 