Best way to fill gap in double glazed sash windows

Hi,

Just stumbled over this forum and hope I can benefit from the expertise.

I'm installing 16mm thick double glaze glass into existing sash windows (replacing 4mm glass).

I've routed out the depth needed and the glass sits nicely however there's only a 4mm depth available to place the beading.

Yesterday I had the idea of routing a 4mm rebate all around the window and then place a 4mm bead in the rebate that sits flush and has full rebate strength. The * are my 4mm bead

Code:

---

-------
      ! ?? **** 4MM BEAD ****
      -------------  ---------------------
                    !  !       
                    !  !    GLASS
                    !  !
                    !  ---------------------
                    -------------
                                !
                                !

---

My question is about the question marks (??) This is the gap between the frame and the bead. I want to fill this up (putty?) and sand and paint so it becomes invisible.

Should I make the ?? a hard but (zero gap) or something like 2mm gap to put the putty in?

What's the best option to stop that space cracking in the future and looking horrible?

Thanks

Peter