Kristen, it is always helpful if your museum has a collections management policy in place that covers issues such as this one. (I can send you a sample, if you like.) Be that as it may, I am wondering at the outset if your museum accepted the artwork with the understanding that it would be sold. If that were the case, it would have been an unnecessary complication to accession the artwork. Again, that is water under the bridge. At museums where I worked, the collections management policies listed a number of alternative means of disposal for deaccessioned items, to allow for a variety of ethical choices for sale (or discarding deteriorated or valueless items).
To answer your question specifically, there was always one preferred means of sale: public auction. That put the transaction at arm's length from the museum itself, of course. Depending upon the type and value of the deaccessioned items, we might employ a local auction company -- in one case, we realized less than $1,000 for dozens of objects. In one unique case, we enlisted an international auction house, and one object reached a world record price. We usually requested that the name of the museum would not be mentioned in the catalog or during the sale itself, but at least once the museum's name was linked to every object we were selling after we had made such a request. In the end, there was not a single adverse comment. Your results may vary.
Please let me know if I may be of further assistance to you.
Best,
Bruce
A. Bruce MacLeish, Curator Emeritus, Newport Restoration Foundation