For under $30, you can get a SAK Rucksack model online with the locking blade and most especially, a longer saw that is very, very effective. The saw can be used to notch wood and pop out larger pieces, as well as cut down saplings if you need to. Bring the SAK along for small work, like whittling and shaping -- the awl on the back is excellent for drilling holes in wood and other items where needed.
A good multitool with an awl, saw, and tough pliers will come in handy, too, as a substitute. Ron and Karen Hood, who are experts in wilderness survival, recommend the Gerber Multilock.
I know they're not sexy like a big fixed blade, but if you can only bring one knife, these are the way to go if you know how to use them to make what you need. Coupled with a large blade that has an exposed tang (in case you need to hammer on it with a piece of wood or other material) -- and you're in golden shape. If customs won't allow for entry into the country with a large blade, then these small knives will be your only truly effective choices, because they are multi-use tools in small packages, and unthreatening to most people around the world.
If you have only one choice of knife, multi-use tools are the best way to go in the wilds, rather than a fixed blade.
Hope this helps,
Wilderness & Survival Skills Forum