You can buy a clip-on lens that will provide a wider angle of view, and you can almost certainly buy one that will be wide enough for your needs (I know that some provide a 180° fisheye view, even — you mention that you don't want this effect, but I mention it as an example of extremes.).
The typical wide-angle lens one sees in 3-in-1 kits* are about 0.6× lenses, and since there's a linear correlation between focal length and field of view, that's easy — you will get about ⅔ more in the frame with one of these. You can also find "ultra wide" 0.45× and 0.3× add-on lenses — although I'd be wary of trusting the numbers precisely. They're cheap, so I'd suggest getting a few and trying them out.
However, it must be mentioned that all of these are effectively toys — they are simple optical designs which go on top of but do not replace the built-in lens, and will add all sorts of uncorrected defects. This may or may not be a deal-breaker for your needs. If you are just looking to review a swing or something like that, it might be okay. If you are making images for a more lasting use or you need to make a good impression with them, you should consider investing in a real camera.
* not an endorsement — just a representative sample.