EEK!
If the striker (firing pin) is tight in the cocking piece, you WILL shear the end of the striker off (ask me how I know) trying to hold it still in a vise.
Make the tool. Piece of steel brake pipe and a file is all that is needed. A Coleman naptha camp stove generator is also the perfect sized tubing.
Or a correctly sized deep socket and a grinding wheel.
Dimensions of the tool are to be found on the net. Literally a five minute job to make one when you know what you are doing.
On high mileage rifles, the threads on the end of the striker can get damaged and peened over making the striker a bear to remove. In this case screw the striker further IN and dress the threads at the very end of the striker, then screw out. Even when the striker starts to move, it can be tight all the way out to the last thread.
What often isn't realised is that the threads on the striker, and in the cocking piece are a very tight fit by design. There needs to be zero movement or play between striker and cocking piece, they need to be locked solid, and the striker straight as an arrow, otherwise trigger pull off can never be adjusted correctly. Hence, only remove the striker when you really must, don't want any wear to the threads. A brand new striker will actually need some torque effort to screw it into a brand new cocking piece, and torque effort to get it back out.
I have a home made tool and often bust it trying to budge a seized striker.
I just file the end of the tool flush and recut the profile and go at it again.
Eventually the tool will be too short, but have used mine ten years already.