How drastically did your station change? How big are these inflatables??
There are a couple of ideas here:
1) Hold on to them!!! Radio stations come & go (some even come back!), but nostalgia lives forever. Never know 10yrs down the line if somebody might want a chunk of history & be willing to make a big donation to the charity of your fundraising choice for it.
2) What's the public opinion of the old station? This really says a lot. If they LOVED the station (why did you change then), desecrating won't earn you points with the old crowd. BUT, let's say it was a very welcomed change.
a) inflate with helium, let go, first person to bring it back gets 1100 bucks and some sort of cool to-do with the new station. Maybe even help design a new logo (but you've probably already got one, huh).
b) Donate it to the homeless for shelter
c) Fill it with gallons and gallons of Pepsi, & drop 10 packs of Mentos in. Launched to moon. No problem.
d) Do the EBAY thing, except just cut out the old logo & auction IT off (charity focus, website driven-- keep it low key).
e) Throw it away and move forward.
d) Get a NEW inflatable & puppet a battle between the old & new in the streets of downtown a la Godzirra. New one wins.