usually the more powerful the lens, then the more shakiness or blurring occures when you use the zoom. Some cameras have a built in "accessory" or feature to reduce or eliminate this. Wife has a older model Sony SLR style digital camera with this feature and it works. I know this type camera is not what you're wanting or needed, but the feature is available, but I don't know if its available on the smaller point and shoot cameras. You may want to look at the GoPro, they are pricey, but from some of the pictures I've seen posted on other fishing forums, nice pics, and don't remember any blurring, etc., but they may be able to edit that out or take several pics till they get a good clear pic.
You might try using a different setting, such as a sports mode, which has a faster shutter speed if your camera has those options. Or portrait mode, etc.
GO BIG ORANGE !
I meant to behave, but there were just way too many other options available at the time.