If you are anywhere in the world and are told to squalk A****, then the controller is using the correct phraseology for a Squalk change. If you have a Mode C to suppliment, then leave it on too, a controller cannot tell you to deselect this unless it is discovered to be corrupt. Remember that the 4 number bit is the Mode A bit.
It is true that by switching to standby in some areas, the radar information associated with the return can be lost and not fully regained without re-identification. You are not 'foreground' therefore not bright green, and just a dull grey blending into the black behind. On a side note too, when selecting your numbers, don't hit the ident button. If you haven't got all four of yours correctly selected, and waited a few seconds for radar to receive the new selection, you may inadvertently process the flight details of an a/c using a similar squalk. Confused? Should see the controller who gets the 'ghost' flight details.