Open a Finder Window.
Select the files you want to print (command-click after the first one, of course).
Use the "Print" item in the File Menu of the Finder. Note it does not have a keyboard shortcut.
Any apps required should open and the selected files should be printed.
I just tested this with a ".txt" file and an ".html" file. TextEdit-Plus opened the text file and BBEdit opened the html file. Both printed just fine.
Of course, all the files would need to be in the same level of any directory. It appears that you cannot select items in different folders at the same time.
Also, the required apps will also remain open. That may not be what you want/need.