Hi Julien,
You should try Motherload. https://www.cartmega.com/software/osticket/motherload-for-osticket.html
Our Superlists plugin for osTicket Motherload is implementing something similar to what you suggest on the new Ticket page (client side).
Basically it identifies and hides various custom fields on the form and replaces them with dropdown lists.
I am positive that you could achieve your goal.
Coincidentally, I just uploaded a new free plugin for Motherload called JSInject that can help to inject custom Javascript into osTicket.
Hope this helps.