I use Puukkos, axes and Kukris.
Not being satisfied with my GB Hatchet - because for its 700gr of weight it didnt deliver enough and the much better SFA is a bit too heavy and bulky to ncarry around all the time - I replaced it with this Kukri:
which I got here:
http://www.toratoratora.co.uk/
Shown is a 680gr WW2 Kukri with a wooden handle. By far not the heaviest one to be had, but the maximum I can use singlehanded.
In the top picture it is shown with the original scabbard, but a "Jagdnicker" and a ceramic-stick (glued into an old filehandle) replace the supplied accessories (chakmak, Karda). Total weight 966gr. The picture below shows it with a sheat of my own design and a SAK, total weight of this setup is 890gr.
Firemaking, building a shelter etc is doable with these sets and weight and bulk are acceptable.
Next in the line is a much lighter Kukri, a "Sirupate" design, weight around 485gr, for which I will make a new sheat with an added pouch for the SAK. Potential weightsaving is 200-250gr ands I have only to pack one item:
For general woodwork, nothing beats an axe like the SFA and LFA, but its not always necessary to carry one (and the knife to compliment it) for more basic needs.
Thats were a Kukri, which can be used as both, a big knife and small splitting-tool, really shines.