Regardless of blame, your insurer should be informed of all accidents so going directly to the 3rd party to avoid them knowing is, technically, risking voiding future insurances should you return to insuring your own vehicle.
If you have a disability, regardless of insurer you should get a suitable car as a courtesy, even if they have to hire one, just make sure you aren’t inconvenienced.
Good luck
I'm Autistic, if I say something you find offensive, please let me know, I can guarantee it was unintentional.
I'll try to give my honest opinion but am always open to learning.
Mark