The shift reg approach has the benefit of "latching" while the 4017 doesn't. Of course the 4017 can run at 12V, the 74xx164 runs at 5V, needing a regulator. Maybe a 4094 SR would do the job instead of the 4017. If you use the 4017, you will need to figure out how to keep the LEDs on, probably via a latch or flip flop.
to be clear, you will need an oscillator to drive any of these chips. the 555 timer should work OK.
I also wonder what current your LEDs will draw vs your relay coils. I suspect that it's easier (and definitely cheaper) to just drive the LEDs directly.= but that's your choice. Note that with 12V you could drive a number of LEDs in series to keep the current down.
Phil