I would like my file type to have an "Edit" button in the FileManager

If you've got a custom file type which you'd like to be editable in the filemanager, it must be considered a text file to the system.  The way DA checks for this is with the mime types file:

/etc/mime.types

The format of this file is the type on the file, and the extension(s) on the right, separated by one or more tabs.

In order for your extension to be considered a text file, it must be present in the /etc/mime.types file, and also have the type starting with text/.

Just as an example, the CakePHP extension is ctp, so you'd add something like

text/x-php     ctp

to the /etc/mime.types file.