My guess is that you also have Adobe's ADDT installed along side WebAssist UE4. The ADDT extension also uses the exact same naming convention as the UE4 for "Delete File" which causes the selection to actually try to invoke ADDT first.
There is an easy fix, see my last post on this thread: showthread.php?t=11500
You will just need to change the title in one file from "Delete File" to "Delete Files". As you may have guessed, the behavior for WA UE4 will now be renamed to Delete Files with the "s". But this will fix your issue.