Hey Michael,
That won't work, because the single listed POSIX Path in the script is arbitrary and has nothing to do with the Finder selection.
What you're looking for is something like this:
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# Auth: Christopher Stone
# dCre: 2018/06/01 20:00
# dMod: 2018/06/02 00:12
# Appl: Finder & Sharing_Utilities_Library (by Shane Stanley)
# Task: AirDrop Selected Items in the Finder
# Libs: Sharing Utilities.scptd
# Osax: None
# Tags: @Applescript, @Script, @Finder, @AirDrop, @Selected, @Items
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use shareLib : script "Sharing Utilities"
use scripting additions
----------------------------------------------------------------
# Acquire the Finder-selection as a list of aliases.
tell application "Finder"
set finderSelectionList to selection as alias list
if length of finderSelectionList = 0 then error "No files were selected in the Finder!"
end tell
# Transform the aliases of the Finder-selection to POSIX Paths.
repeat with theFile in finderSelectionList
set contents of theFile to POSIX path of theFile
end repeat
begin AirDrop with finderSelectionList
----------------------------------------------------------------
Unfortunately I can't test this, because my 17" Mid-2010 MacBook Pro doesn't support AirDrop.
Let me know if it works for you.
-Chris