As has been suggested a bath in i.p.a. would be a good idea, with a
gentle scrub with a brush. With the batteries out you could bake it at
80Deg.C to dry out any water.
Water and detergent won't damage modern electronics as long as it's not
powered up.
Unfortunately your fob was.
Are there any blue-green deposits anywhere. pth holes and via's can be a
problem especially under chips as any conformal coating tends to miss
those areas.
--
Neil J. Harris