Considering the oak on it's own when not actively transmitting is only consuming around 15-50ma depending on load as opposed to worst case 220ma, but more likely around 115ma when transmitting, that should be of itself enough of a power saving... You can get it down to 1ma if you suspend the CPU (so no reboot when waking up), or 50-70ua via deep sleep, but then as defragster pointed out, you will have to go through the whole wifi renegotiation at power up, so it's not worth the hassle. Factoring in 120ma power consumption per hour (and will probably be a little less than that if you are pulsing at 0.5 second intervals instead of continuous), you need roughly 960ma of power for 8 hours. I reckon a single cell 2200 mAh 18650 lithium battery should do the job with a decent reserve. It depends what else you need to stick onto the portable device.
EDIT: Oh, and btw, SYSTEM_MODE(SEMIAUTOMATIC) will prevent an automatic connection to Particle, but still try to connect to the registered wifi network. SYSTEM_MODE(MANUAL) will prevent both automatic connection to wifi, and connection to Particle.
Have a look here if you want to see more on that - since you're not interested in Particle for this application, the SYSTEM_MODE(SEMIAUTOMATIC) mode may be desirable as it would have some power-saving effect due to not looking for Particle, and the Oak would be more responsive as far as time sensitive code.
Pete