Mora knives are the perfect solution to your problems. There might even be cheap (er) chinese copies that might do the trick.
If you have relatives in Sweden or know someone going over there, ask them to go in to any hardware store to pick up a bunch. You can get Hultafors knives for about 5 bucks and Mora knives for about the same price. Go for quantity, not quality. One Mora 2000 cost about the same as six or seven regular ones. Usually when you buy something else, like wood for your gazebo etc. they throw in the Moras for free.
And remember, a Mora is expendable. If it gets dull like a stick or breaks, just pick a new one.