There are a few ways you can do this.
The industrial-strength method would be to use something like memcached but it sounds like this may be overkill for what you need.
A simpler method would be to make your query and then serialize the array to either the filesystem or to a database table made to store cached data.
Then you only have to unserialize the data to have the array back in its original state.
On your management side, when the contents of the dropdown change, you can re-create the serialized array.
Wes