High-end sushi chefs in Japan prefer to use rubber, rather than wood, cutting boards. They don't require constant oiling, are said to be gentler on knife edges than wood, and still pass the all-important hygiene standards. Additionally, the rubber surface means the fish doesn't slide around as you slice it. However, there are two drawbacks with rubber cutting boards: They're extraordinarily heavy, and they cannot be washed in a dishwasher, as super-hot water will deform them permanently.
To get around this, manufacturer Hasegawa produces a rubber cutting board with a solid wood core. The edges of their Soft Cutting Board are sealed with polyethylene. Using wood in the middle reduces the weight by 30%, and allows you to wash the board in a dishwashing machine without fear of warping, as the wood retains the shape.
You don't have to watch this video to understand what the cutting board does, but it does give you a better look at it. (You might also be amused to see that sushi chefs cut on the pull stroke, as do woodworkers in Japan.)
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In the U.S., they're carried by retailer MTC Kitchen, and they're pricey as heck. A roughly 12"x24" runs $140—and wood core aside, still weighs 5.3 pounds!