I did the same thing to replace my drivers door handle.
Removing door lock cylinder without key.
Then you can pull the lock cylinder tumbler out the other side.
I didn t get a key with mine either.
Use the flat head screwdriver to turn the spindle in the center of the door lock cylinder counterclockwise until it stops.
At this point the square tab on the spindle is aligned with the square.
You must be able to do it without the key.
Look for a small set screw at the base of the handle.
In case you lack the original key you have to replace the complete ignition switch assembly instead of just the lock cylinder.
As automobile keys are complex picking a chevy lock cylinder is much more complex than a regular doorknob.
Open the door and look for the latch plate along the door s edge.
How to remove a door lock without a key.
I think there is a roll pin on the back of the tumbler that holds it all together.