Bit late with this reply, so perhaps you might have already got an answer elsewhere.
I have used a TZ20/ZS10 with a red filter, but I'm not sure I understand your question because it appears to cover two different issues - exposure and colour balance.
I assume you were first using the 'underwater' preset because it gave you more control over white balance than in any other mode. The latter is not quite true. This preset makes the WB control more accessible, but just as much manual adjustment of white balance is possible in other modes, including P.
You are now thinking of using 'manual' mode but fear losing the ability to control white balance and are thinking that a red filter might help.
My understanding of the ZS3/TZ7 is that it doesn't actually have a true 'manual' mode. Since you mention the ability to control shutter speed, I'm thinking what you *really* mean is adjusting the 'minimum shutter speed' setting in the Program (P) mode; and you want this maybe because your pictures have some motion blur?
My answer is therefore in two parts. Simple one just to answer your question about whether the red filter will work. The longer answer below that assumes that my reading of the problem you have is correct.
1. Will the red filter work around work?
Answer: only sometimes. You are replacing one problem (slow shutter speed) with another (less light into the camera and fixed alteration of colour balance). In good light conditions and at the right depths for the correction of blue cast, it will work out. Otherwise you will still have to 'fix' the photos after with photoshop.
2. The long answer:
To freeze motion, you need plenty of light. The built in flash only has a useful working range of 2 - 4 feet underwater and suffers another problem of backscatter. Adding an external strobe will give you one solution - enough light and with the right colour balance.
Second best is to reserve your flash for use in close-ups (macro) and then use P mode & minimum shutter speed set, with or without the red filter, for everything else including video. Essentially you are shooting using ambient light and therefore will get better results if you also periodically reset your white balance, say for every 10 feet of depth. Closer to the surface and with near objects, you won't need a red filter. Deeper or for subjects further away, the red filter will compensate for the blue/green colour cast. Just think about the overall path the light has to take through water to get to the subject then to your camera - the longer the path, the less red there will be. The filter rebalances by removing blue and green, and so you want just enough of this effect for your camera to do the rest of the white balancing itself.
Manually setting the white balance (against a white object underwater with you) will provide much better results than the red filter. You will probably find that you end up using the red filter fairly rarely and mostly for video.
Final points to remember:
a) The camera 'knows' when you have a custom white balance set and will automatically override it to a 'daylight' setting when the flash is triggered.
b) The camera doesn't know when you have a red filter over the port. So if you set the flash, everything will go red. If you switch to flash or strobe, you *have* to take the filter off.
For the above reasons, I eventually gave up using the red filter and got myself more and more used to setting white balance underwater. Now that I have upgraded to the later TZ/ZS models which allow you to 'save' the white balance to a 'Custom' mode, I have this all set up to a depth of 30 - 40 feet, even before I travel!
