From experience I find that one tool (read knife) does not cover all contingencies, yet being without at least one knife outdoors is sheer folly.
Here is what works for me for an extended time and I certainly agree about traveling light.
1. Spetznatz shovel (with cover) Don’t think so? Try digging a hole with any knife you have. Additionally this shovel is generally light with sharpened edges and the handle can be wrapped in paracord.
I keep one in my car/truck and it has helped me out of some jams.
Oh yeah, you will get into jams too. Just accept it and adapt.
You would be surprised how useful this tool/weapon can be if you ever carry one.
2.A kukri of some kind. (I found this not so necessary if I have a Spentzatz shovel with me.) A kukri is a proven design throughout the ages. Generally these knives are heavy yet necessary for what they can do. The additional small knives that accompany are very useful. Not good for children or older people due to the weight but definitely useful and formidable if you can handle. Check around as there are some lighter kukris like Kabar.
3. Mora field/neck knife. Very practical, light, handy and useful for many daily tasks… as is carrying the
4. Victorinox Spartan model Swiss army knife.
Leatherman has been suggested but I find not much useful if the above are available.
Numbers 1,3 and 4 above would be my minimum carry for any extended stay with #2 as a backup if I could carry.
Hope this helps.