The family members obtain the shark's skin fairly early on in the book. They are excited by the possibility of its being a valuable tool, and we are told that they believe the skin is rough enough to use as a file.

Let us try if we can induce these greedy birds to spare us a bit of the shark’s skin; it is extremely rough, and when dry may be used like a file.

Shark skin is rough if rubbed against the grain. A shark's skin doesn't contain scales like other fish. Instead, a shark's skin is made of tiny, hard, tooth-like structures called dermal denticles. They are asymmetrical, and feel smooth when moving your hand from nose to tail; however, they are rough like sandpaper when felt tail to nose. The family doesn't use the skin as a file like they initially hypothesize, but the family does adapt the skin in a way that aids them in tree climbing.

So saying I held up buskins of shark’s skin which I had previously prepared, and which I now bound on to their legs. Thus equipped they again attempted the ascent, and with a loop of rope passed round their body and the trunk of the tree, quickly reached the summit.

In this book, the family takes all sorts of things that they get from nature and puts them to good use.  For example, at one point, they kill a porcupine and they end up using its quills for needles and for the tips of arrows, among other things.  The shark's skin does not get used for anything so vital (at least not that we are told of).

In Chapter 2, Fritz shoots a shark.  In Chapter 3, they come across the dead shark and the father tells them to get some of the skin because it can be used like sandpaper or a file.  However, we never see them actually use it for that purpose.  Instead, the only time we see them use the skin is when they wrap it around their legs to help them climb trees more easily in Chapter 7.