Hi Ian,
Adding resistance does not buy you anything, and can actually cause problems with device startup. Adding the resistance to the supply connections can starve the device from necessary startup current demand. Also, you will add a voltage drop across the resistances and will also consume power.
You could use an external clock source that is slower and that can be shut off. Remember that the slower clock means slower communication and the digital filter response/data rate will change as well.
Best regards,
Bob B