I have a lot of wood veneer that I would like to cut into strips.
I need the strips to be accurate, and I need the strips to have
a 45 degree bevel on the edge.  How should I proceed?
Bandsaw?  Table Saw with what kind of a blade?  Router? Hand Sander?
The veneer is very thin [1/32"] and very fragile.

I am rather practical but now a woodworking specialist, and this is
just a free comment.
I would clamp the veneer between two pieces of press-board or the like
and saw it with a table saw with a fine blade  -  tilted to 45°, of
course.
"Clamp":  screws not extending through the bottom board.

This a is a bit generous with material,but the result is what counts.
If this works, you would have your 45° cuts on both pieces of veneeer-

Myoarin

YOu might try using a paper cutter, but make sure the cutter does have
a clamp wich willl hold the venner in place in order to get a straight
cut (I personally used a paper cutter when I used to work with veneer
fro approx. 5 yers ago, and it worked very well for me)