I understand you would prefer to change ther batteries rather than the whole siren unit. I had the same thoughts with mine.
However, i would say there's a 99% chance your circuit board is corroded beyond repair. I recommend you perform an autopsy on your unit to check ther circuit board before trying to source replacement batteries.
I changed mine a few days ago, photos attached.
Note: my car hard always been garaged and very well cared for so no crossfire is immune.