How to accurately cut plywood with unpowered hand tools?
First off be aware of a couple of important points.


In the old days before there ever was electricity and power tools crafts persons could build amazing things out of wood with hand tools alone.
Woodworking, similar to any other craft, takes patience and practice.
Plywood material such as you are proposing to work with is a modern thing invented in the age of power tools.


So yes you should be able to achieve your goals with hand tools if you take your time and work carefully. If you find any step of the process not going quite right slow down and practice till you perfect the skill for that process. 

You should be able to cut the plywood with a good sharp handsaw. Plywood is a challenge though because you are simultaneously cross cutting some of the wood layers and rip cutting others. Hand saws are typically optimized as a cross cut (across the grain) or a rip (with the grain) type saw.

To get the best smooth cuts on plywood most folks will find that a power saw equipped with a carbide tipped blade will do the best job. This could be a portable circular saw if you measure for and setup a straight edge guide to run the saw base against you can end up with very good cuts. 

The downside of hand cutting plywood is that you will invariably end up with a fairly rough edge. Sanding to get it smooth can be done but sanding has its problems because you can end up with a non-straight edge that may be rounded off. A hand plane may be a better choice but plywood is also a challenging material to hand plane and it is easy to get edge splintering when planing plywood in this manner.