Hi,
Two extremely important informations are missing:
* timing of the pulses
* expectable current (waveform)
... urgent to decide how to control the valve.
Some remark about not using a microcontroller:
* if you want a positive , then a negative , then a positive ... pulse --> then surely you need something to "memorize" the last pulse direction. If this is the job of "the electronics", then you can´t power OFF it completely. It needs a supply .... in most cases.
* current consumption of a modern microcontroller may be reduced by some power saving modes. Usually there always is some kind of power saving mode, which means a current consumption below some microamperes.
If I had to design it, I´d surely go with a microcontroller. It could be a simple 8 pin one using the internal oscillator, thus you have low part count, while being very flexible with software.
Klaus