Issues replacing ignition lock cylinder

Hello and welcome to 2CarPros.
You have a classic automotive catch 22. Let's see if we can help.
First, you have the key for the one that is installed but it is stuck and won't turn? Or you did get the old one out and the internal switch turned and locked?

If it's the first one, does the switch move at all or does the key just go in and not move? Did it just stop working one day or did something else happen? Asking because there are different options if the switch was damaged or if the key just doesn't work.
If it's the second option you will end up replacing the entire steering module because the steering lock will get damaged if the switch moved without the cylinder in place. It's also the reason the key has to be moved to start to remove the cylinder, if the cylinder is removed in the off position it damages the lock itself.
Being a stick shift you shouldn't have the lock solenoid to deal with. You might try calling a locksmith, if your issue is from a worn key or internal cylinder damage they might be ably to get it to release and swap out the cylinder. Then you still need to get the replacement keys coded into the system and most of them can do that as well.