I have an old bass clarinet I haven't played for years. I opened it up and it smells really musty. The reeds were icky so I threw them out. How do I get the smell out without damaging it? It's not mouldy, just smells of cellar.
I find that the mustiness smell mostly comes from the case. I'd suggest vacuuming the case then leaving it out in the sun for a few hours.
For the instrument, wipe it down with a dry rag or paper towel. You can get any of the dust out from between the keys using a small soft paint brush or q-tip.
If the smell still does not go away and it seems that it is the instrument itself that is the problem, the clarinet is in need of a repadding and should be taken to a repair shop.