Make sure it says plastic safe on the can. Deoxit D5 is awesome but very expensive. CRC QD Electronic cleaner works well and is cheap. You can also use a Scratch Pen/Brush to clean the metal.
I would use a fiberglass scratch brush to remove the remove the solder mask by the battery terminal near R469. The 2 diodes near the other side of the battery should be removed to clean up that area. The Amiga will run fine without those diodes since they are used to charge the battery and power the clock circuit.
Overall the damage doesn't look too bad. I'm currently working on an A3000 with more extensive damage.
I've used something like this at my job to clean corrosion on the pins of old NES games
https://www.amazon.com/Economy-Scratch-Brush-Fiberglass-Inches/dp/B0058EDPZU
might work for you