Well, one of the reasons for buying something like a G16 is so that you DON'T have to use a filter. Return the filter if you can. I would recommend shooting everything underwater in RAW and correcting the white balance in post. You can also manually set the white balance, but why bother for stills? For video, I always use manual white balance. You can also use the underwater setting for video, but that's only good down to around 20-30 feet depending on the ambient light.
Here's how I have mine set up: I use C1 for video, and have it programmed for manual white balance with the lens zoomed in just slightly. I wear white fins, and adjust the white balance once I hit about 30-35 feet. That usually keeps it good enough to be able to tweak right in in Lightroom. Above 30 feet or so, I sometimes switch to the underwater white balance setting. If I go much deeper than 50 feet or so I'll readjust the white balance. I try to keep it set so that if something cool comes shooting out of the murk I'm ready to go. I also have C1 set up for manual focus, as you will find that the G16 tends to hunt for focus in video when there isn't a lot of contrast. So far, it has worked out super. I set it, programmed it in, and never mess with it.
I have C2 programmed for stills with the lens zoomed to about 50mm. I shoot in RAW with the white balance set to auto, because I use strobes. That way, the .jpegs look fairly normal. If you try using manual white balance with strobes, the .jpegs will look terrible and be useless.
You want to try to keep the button pushes, etc to a minimum while you're diving. Play around and find the settings you like, and program them into C1/C2. I also programmed the shortcut button to AWB, so setting the white balance is two quick button pushes.
---------- Post added June 26th, 2014 at 03:58 PM ----------
P.S. Another thing you'll find with the G16 is that is likes to overexpose by about one stop. You can adjust that with the exposure compensation dial or fix it in post. I haven't figured out a way to change it for video, so I run mine through Lightroom and adjust it there. You can get some absolutely AMAZING video out of the G16 underwater. Run it at 1080p 60 fps and if you travel, buy a large SD card or bring a computer.