You can use tablet sweetener but not granulated. I asked my CDC why this is and apparently, surprisingly, it contains something that does not aid digestion and it stays in the system longer - so it cannot be flushed away as easily.
I use a tablet sweetener in my porridge but the heat from the hot water dissolves it. I have no idea what a tablet would do in cold water - my suggestion would be to dissolve a tablet in hot water and then let it cool (unless you like hot shakes!!) - but I don't know what that would do to the flavour - I don't have any shakes at all.