You are missing the tiny detail that metal is not the only material which can provide sharp, cutting edges.
The reason the Stone Age got its name was the use of stone for tools. Both flint stone and obsidian, a volcanic glass can splinter with razor-sharp edges. Both the raw material and the tools made from them were highly prized goods and mined and traded in prehistoric times.
Even today, obsidian scalpels are still used for some surgical procedures, especially in cosmetic surgery. What works for a face lift in Hollywood should easily be good enough for pemikan - not that I'm comparing the two tasks.
Failing to obtain the stones, bone knifes from long leg bones would also have been able to handle the task of cutting thin meat strips quite smoothly.
Not for the squeamish:
This Youtube video shows the butchering of a deer with a simple, hand made obsidian "knife".
This video compares a flint and a bone knife.