In my opinion - with water (can be distilled) and then dry the whole thing. Don't be afraid to dip the plate in the bath. After drying, you can (I would for sure) wash everything thoroughly and on both sides with a cloth moistened with alcohol. After such a procedure, everything will be OK. Sugar is not a very good conductor of electricity, but hopefully when the disaster occurred the batteries were removed from the remote immediately.
Good luck cleaning the tile with water. Only pure alcohol (spirt, plywood). However, rubber can be under water. I do it with warm water + dishwashing liquid + hand brush.
