Sally,
     Greetings from Nebraska.  You say the trophy heads have data.
I'll presume they all test positive for arsenic or other nasties.
Contact the nearest, and these days you usually don't have to go too
far, DNA researcher and find out if the tanning process wipes out the
usefulness of the specimen for DNA work.  If it doesn't then find out
how much hide (fur and all) would make an adequate sample.  Remove
that much, or twice that much, hide and note the change from taxidermy
mount to skin sample.  A photograph would be recommended for record.
     The remaining piece, horns/antlers and hide, and be disposed of
various ways.  Horns/antlers to learning centers from Kintergarden to
College Mammalogy, the U.S. Fish & Wildlife forensics lab in Oregon
would love hair samples for comparison of suspected illegal imports,
right back to shipping the specimen to the original country as
educational material in their museums in exchange for more pertinent
material you need.  Glass eyes,particularly antique ones, are usually
snapped up by taxidermists, maybe in trade for cleaning and remounting
of material you do want to keep.  Contact the local hazardous
materials program for proper disposal of head forms, etc.
                Good Luck
                        Thomas Labedz
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