I’m not on a Mac at all, and just took a guess at an auto file joiner for the files at http://www.box.net/public/nkbz9482nv#f3386748 for which I’ve already done windows and linux joiners.
My attempt is really just calling the equivalent of bash shell commands, feel free to make corrections/completely rewrite it 
do shell script "cat 1998-12-29_WRUF.mp3-0.vsplit 1998-12-29_WRUF.mp3-1.vsplit 1998-12-29_WRUF.mp3-2.vsplit > 1998-12-29_WRUF.mp3"
do shell script "rm *.vsplit"
do shell script "rm merge-*.*"
I’m really just after whatever will work that I can also adapt for other similarly split files (they limit file upload size to 10MB)
Cheers!
Usex
Your do shell cat command should work.
I tested this with a couple of mp3 files from the site (not .vsplit)
and worked fine.
Remember to use the full path of the files.
I did not test the RM
I was hoping it would work without paths if it was run in the same directory as the split files 
So… how to obtain/use the full path that someone chooses to download the files and script to?
A very quick example.
set the_c to ""
set these_files to choose file with multiple selections allowed without invisibles
repeat with i from 1 to the count of these_files
set this_path to (item i of these_files) as string
set this_item to POSIX path of this_path
set the_c to the_c & (quoted form of this_item) & " "
end repeat
tell application "Finder"
set this_path to this_path as alias
set this_item to (container of this_path) as alias
set this_path to POSIX path of this_item & "test.mp3"
end tell
do shell script "cat " & the_c & " > " & quoted form of this_path