Not in your housing, you can't adjust it.
Basically for those that can, MWB is a process of "telling" the camera what's white at depth so it can adjust colors accordingly to compensate mostly for the excessive "blues" found at different depths or conditions. With a camera/housing that can do it, you push the MWB control while filling the screen with something white so the camera can adjust itself. Sand, sun, white Apollo fins, dive slates all are options.
Housings that can do this are Ikelite, Ocean Images, Gates and the L&M BLueFin (there's probably others) They all provide a manual control to press the LCD touch screen. You can re-assign the menus on Sony cameras to make the MWB screen a default option when housed for easier access.
Your HC7/9's Auto White Balance continuously as does mine, I've been pleased with the results generally. Deep low-light conditions do have excessive blue saturation but I don't have lights.
I've had mixed results powering the camera off/on at various depths as from what I've read, Sony cameras white balance on startup. I may be just kidding myself that it does anything however.
I did try once powering on my camera while holding a white Expodisc in front of my port, after a couple of days of experimentation, I re-sold the Expodisc - it just didn't seem to be any better.
If you're reading in the other post about MWB with an EVO and A1U, they're able to do that since the camera has a MWB assignable button. Amphibico provides a manual control to push it as an option on an EVO. Your HC9 doesn't have one.
How's the new toy?