You could do that but it wouldn't guarantee that the first wouldn't oscillate. You would still need a properly timed pulse. For a 2 second delay you would need two 555's (or one 556), one for the 2 second delay and the other for the 4ms pulse.Question : Could I put the one-shot to control the delayed operation (2 sec) of the first relay AFTER the second relay is switched directly (no delay) ? This would seem like a safer way to guarantee that they don't vibrate and the timing would not be so critical.
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Actually since the relay only requires 4ms to operate you wouldn't need a delay longer than about 10ms for the first one-shot.
Note that you need a reverse biased diode across all relay coils to suppress the coil transient spike that could zap the 555.