Perhaps I'm making this more difficult than need be. This is just how I would approach it using WavePad. I do work like this all the time, albeit in the reverse (splitting up long files into tracks.)
If they are labelled in a chronological order, each file should have it's own tab along the bottom of your workspace in order from left to right.
Start with file 'A'. This will become your final file. Add your silence, and re-name it 'Master file or something.'Re-naming it will create a new file, and preserve the original version of the file.
Now click on the B file tab which will make that the open window, add silence, select all, copy. Click on file A tab, position cursor at end of the file, paste.
Now I would click on file B again and close it. The program will ask if you want to save the changes (you added silence) choose either save or don't save.
Closing the files after you have pasted them into the new project file will help keep track of where you are.
some tips: when positioning the cursor, sometimes you can inadvertently 'select' an area, as opposed to just a static cursor. Zoom in to see if anything is highlighted.
remember that the clipboard with hold the last file/selection, until you 'copy' something else.