I have no answer to your question, but want to provide information anyway...

The lens in the SJ4000 isn't identical to the GoPro, so you won't succeed in "removing" the fisheye, depending on what you expect out of it, unless maybe all you expect is "it looks better to me" in which case it might, as they are similar. The main difference seems to be that, in both photo and video mode, the SJ4000 fails to utilize the full field-of-view of the lens, but other than that I think they're rather similar.

However, I think the "betterness" of non-fisheye projections when combined with wide fields of view is entirely debatable. Common projections (what you're used to seeing) preserve straight lines, but do a terrible job of preserving the shape and size of objects that aren't in the center of the image, and tend to create a "objects are closer than they appear" effect, with both problems being dependent upon how wide the field of view is. Fisheye, on the other hand, doesn't care so much about straight lines and instead does a better job of preserving the shape and size of objects even with wide fields of view.

I put together a small web album to show what I'm talking about, which I should probably post to imgur since I always delete junk off of my web site after a month, but posting complex things like a web album on my web site is just so much easier... My apologies to people who read this post more than a month from now.

There's four copies of each image. The first is a photo straight from my GoPro Hero, the second is that photo processed with a "fisheye removal" tool I wrote. The third image is the same processing, but without the image cropping applied, so that you can see just how ugly standard projections get at the extreme edges of the field of view. The fourth option is another lens transformation I created as a sort of compromise between the two.

If you look closely, you'll see that fisheye isn't the only projection with faults, instead it is just that you're used to the faults of common projections and not used to the faults of fisheye projections. The most obvious example is the last image in the album, where the fisheye version makes it obvious that the cupboard doors are each half of the width of the cupboard itself, but the common projection makes it look as if each cupboard door might be able to cover the entire cupboard individually, especially when you look at the non-cropped version. The only reason you don't normally notice this is that the amount of distortion depends upon the angular distance from the center of the image, and most photos you see aren't taken with wide-angle cameras. However, it is readily apparent in a lot of video games, especially ones which allow you to crank up the field of view to 100° or so.

There are other faults in the other images as well, e.g. look at the two-liter bottle of soda at the bottom-right photo of the fridge. It looks OK in the fisheye projection, but the bottle shape is obviously distorted in the standard projection. The same goes for the plate hanging on the wall in that same photo. Also check out the cigarette box at the edge of the table in another photo.

The reason these wide-angle cameras use fisheye is because it really is the best lens for wide-angle photography.

...and there's good news: Give yourself a couple of weeks to get used to it, and the distortions in the fisheye photos will look as normal to you as the distortions in the common projection photos. Hence why I never updated this tool to similarly process SJ4000 photos: By the time I'd bought my SJ4000 (about a month after I bought my GoPro Hero), I had gone from hating fisheye to loving it, and so I had no desire for such a tool anymore.

Fisheye is awesome. Just give it a chance and you'll love it too.