If you're hiking forget about anything like an axe, its way too heavy.
In my opinion, you need three basic cutting tools - a small to medium size fixed blade (3" - 6"), a locking folder, and a folding saw. If for some reason you need to build shelter etc., the folding saw is by far the most efficient tool for the job. In my opinion this forum pays far too little attention to them.
Second thing - a knife is not the only thing you need for survival. You must also have with you at least 2 methods of creating a fire (firesteel / lighter / waterproof matches) as well as dry tinder (cotton wool dipped in vaseline is good), cord for shelter building, a whistle, a signal mirror and water purification tablets. Also take a map and compass, and plenty of water. The other crucial thing is a first aid kit.
Please don't assume that these things are only for the survival enthusiasts who frequent this forum, and that you won't need them. It is not hard to get lost when you're inexperienced, and these few simple things are the difference between life and death if you get lost in the backcountry.
Take care and have a fun trip.