Watch cleaning, my favorite topic.
For rubber strap, clean the side that touches the skin with soapy water and rinse it with clean water. Use a soft toothbrush and brush gently if you have to remove salt or soil deposits in small and hard to reach areas. Instead of soapy water, I have used Neutrogena clear shampoo mixed with water with great results. That Neutrogena can remove oil and grease really well.
To keep the rubber strap looks moist and not dried out, apply Lexol Vinylex to the top side of the strap, indirectly with a cotton towel.
I use the above techniques on my Galapagos every now and then.
To clean any metal watch cases (i.e. steel, gold, platinum, titanium), I use pre-moistened lens cleaning tissue, such as the Bausch & Lomb Sight Savers tissues.
Good luck.
Blue