WBCHSE didn't have any official declaration about the process of application for Re-examination. So I would recommend you to contact the Higher Secondary Board office to get your facts clear.

For WBCHSE contact details you may follow:

https://wbchse.nic.in/html/contacts.html

Now, another thing what you can do is NIOS. This is a Open Schooling which you can give in order to get a fresh certificate from NIOS. The board is authorized centrally so your marksheet will be valid for all kind of examinations and Admission.

To know about NIOS you can visit the link provided below:

https://school.careers360.com/exams/nios-class-12

For NIOS official link you can visit:

https://www.nios.ac.in/

I hope this answer helps. All the very best for your future endeavors!