tell app "Finder" to open file x using application file id "CARO"
Not sure, but I think the identifier is “CARO” for any Acrobat version since ancient times. So, I would write something as:
set identifiers to {"CARO", "prvw"} --> Acrobat, Preview, add more if you wish
set x to alias "path:to:file.pdf"
repeat with i in identifiers
try --> will error if not found, and will try next identifier
tell application "Finder" to open x using application file id i
exit repeat
end try
end repeat
Anyway, you can tell those haters they can just choose their favorite app in the Get Info window of any PDF doc, Open With, then Change all…