CJam, 18 bytes
ea_:gs{q}?'_,_eler
The list of files must be supplied in form of URLs, which is the only format CJam understands.
Example runs
$ cjam kitten <<< "AaÁáÄä"
aaÁáÄä
$ cjam kitten file:///home/dennis/kitten file:///home/dennis/kitten
ea_:gs{q}?'_,_elerea_:gs{q}?'_,_eler
How it works
ea Push the array of command-line arguments.
_ Push a copy.
:g Retrieve the contents of all files with those URLS.
s Flatten the resulting array of strings.
{q} Push a block that reads all input from STDIN.
? Select the string of the array of args is non-empty.
Otherwise, execute the code block.
'_, Push the string of all ASCII characters before _.
_el Push a copy and convert it to lowercase.
er Perform transliteration.