Alternately, one could throw your pulse through a large value capacitor, in series with the relay coil. For all intent and purpose, caps only pass AC and will block the DC component. So even if you use steady high/low signals to power your relay, the relay would only see that initial pulse. You just need to make sure the cap is high enough value and low enough ESR that the required amount of switching current is sustained for the required amount of time.
This is a passing thought/answer, the values required may be to large to be practical. I haven't really done the math. More experimentation may be required.
Edit: Looks like that's probably actually what alec_t is already saying, so... ignore me?