A good quality pen knife would be great IMHO.
They are hard to find.
Amyway, since most people I know carry a pocket knife if they carry any extra gear at all I think the best knife for a PSP is a good decent small pocket knife.
Not a combat, tactical or an assault something or other, just a small folder like your granpappy always had in his pocket to cut a string, whittle on a stick, or slice a chaw a' tabacca off the plug of tabacca he always had with him.
Something with stag or bone scales and well rounded nickel silver bolsters and good springy high carbon steel...
Think about what the people carried before and why. There was a reason a pen knife was called a pen knife and why small folders were often known as stockmen's knives.
In your grandparent's time people people carried small knives like that because they used them constantly, for everything from castrating steers and cutting binder twine off haybales to sharpening pencils.
It might be a good time to look back at the older designs that were dictated by the needs of people who actually used them a lot.
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May set off to explore without any sense of direction or how to return.