Is there a hot key combination that will prompt "Save for Web & Devices.." interface for the clipboard content?
No. For Save For Web to work, you must have document window. Save for web pulls the image data from the active document, and can't pull data from the clipboard.
However, you're probably aware, Photoshop stores most document data on the clipboard. So all you need to do is - New FIle, Paste, Enter Key, Save For Web, Save, Close. (Command-N, Command-P, Enter, Command-Option-Shift-S, Enter, Command-W, D)
Alt + Shift + Ctrl + S you can also customise your hotkeys