Grounding GPIO 3 will boot it up OK, assuming the power supply is plugged in etc.
If you edit the config.txt file and add dtoverlay=gpio-shutdown to it grounding GPIO 3 will have Raspbian do a proper shutdown. Normally that pin would be used for i2c, I have no idea what might happen with the way the Hyperpixel uses that pin? Or what might happen if you try to use another GPIO in use by the Hyperpixel? I don’t think you will damage naything but you might get some weird effects on the screen?
The dtoverlay entry can be set to use another GPIO pin for shutdown. I use the following with my Fan Shim
dtoverlay=gpio-shutdown,gpio_pin=17,active_low=1,gpio_pull=up
The Fan Shim Button grounds GPIO 3 and 17 when pressed.