Reddit mentions of Hults Bruk Akka Foresters Premium Outdoor Axe

There are a ton of axes out there that fit your profile straight out of the box. You're just looking for a European style forest axe.

This is your best "budget" option.

These

are

some

... pricier options.

Don't ruin a perfectly fine American axe trying to replicate a European axe. There's no reason for it.

As for whether your design is good for "camp tasks," well, that depends. You'd need to define some things.

1. What kind of camping? Are you driving out or hiking? If you're driving out, don't fuck around. Bring a full sized axe.
   
   
2. What kind of "camp tasks" are you going to be doing? If you're just going to be limbing for smaller firewood, then even a hatchet will do you well. If you're going to be felling, bucking and splitting whole trees, then car or hike you're better off with a full sized axe. Bucking is a ton of work and a heavier axe helps the tool do the work rather than your arms. If you watch this dude's axe content, you'll see that even he (who prefers smaller axes) does note that you really have to whip smaller axes to get the same effect as a larger axe.
   
   
3. What kind of wood are you working with? If you're working with tough hardwoods, American axes are made to deal with that type of wood better than European/Scandinavian axes that are mostly tooled towards pines and other soft woods.
   
   
4. How much experience do you have with using axes? American axe patterns tend to be a little more forgiving of bad technique since they're bulkier and often not hardened quite as much. (They're still heat treated, but a softer edge is easier to sharpen though it does dull faster.) European axes tend to be a bit harder, but that means they're harder to sharpen and if you chip them (say, on an overstrike or an imperfection in the tree) they're much harder to work out.