I use quite a few knock down connectors, including the Lamello Clamex S18 (yacht fit outs often require cabinets to be brought in through small hatches, so assembling in situ becomes the norm).
It's probably my most used KD connector and I rate it very highly.
I use it with an 8mm blade fitted in a Lamello Top 20. The Top 20 (and the newer Top 21) have the facility of moving the cutter head up or down by 2mm, in order to centre in slightly different thickness components. But it is possible to take advantage of this facility to use 8mm thick Clamex S18 connectors with the standard 4mm thick blade, you wind the blade up to the highest setting, cut the slot, then re-set the blade to the lowest setting and re-cut the slot. Voila...an 8mm slot from a 4mm blade!
Bottom line is I see no reason why you couldn't do the same thing with a 4mm spacer and a 4mm blade.
However, you may not need any of this faff, I believe Lamello now has a 4mm thick knock-down connector. I've never used it but that may be an easier solution for you. It may take some tracking down though, as Lamello seem to focus on their Zeta system with the "P" rather than "S" connectors.
Good luck!