Carbon steel - yes, convex grind for survival purposes - yes, full tang - yes, thickness more than 3/16" - yes, length - I would say it depends. If you have all previous features than you are ready for processing wood, length in that case only determines how wide logs will you be able to process. Bravo 1 is maybe one of the best choices but I can't help the feeling that 4 1/4" is too short.
One more thing. If you rely on this knife as a one option tool, which mans chopping besides splitting, than heft if what you should be looking for as well, and that translates to knife weight. You would need a heavier knife.