I can't find any pulse relays with low voltage coils, or at reasonable prices anyway.
(There are such as selectors and motorised rotary switches, at crazy prices).
The Tycho one AnalogKid suggests does appear to be suitable.
Other than that, the simplest circuit I can come up with uses two, dual coil bistable relays plus a changeover button, or a normally open button plus a simple relay with a CO contact.
The basis of that is a "master-slave" bistable. Each relay has the two coils connected to the NO and NC of a contact on the other relay, with common of that contact fed from the button.
The other side of the coils go to NO and NC on the same relay (as the coils) with common to 0V.
When power is applied, the "working" relay will take the same state as the other relay, shutting off it's own coil power as soon as it changes over.
If you duplicate that, cross-connected between two relays but with the control contact NO/NC reversed on the one fed from the button NO, the effect should be that the first relay changes state when the button is pressed and the second relay changes to the same state when the button is released.
The only power consumption is as each relay changes.
One of the relays needs to be a four pole type to control the external circuit, as two changeovers are needed in each to provide the basic function.