Coat a straight-sided pan with the vegetable oil and set over medium heat. Add the ginger and scallion whites and cook until aromatic, 3 to 4 minutes. Add the rice, sprinkle with salt and cook for a minute or two to toast the rice. Deglaze with the sake and cook for about a minute to allow the alcohol to burn off. Add a few ladles of hot stock to the rice, just enough to cover, and cook, stirring constantly, until the rice has absorbed the stock. Add a few more ladles of stock and repeat. You will do this 4 to 6 times, until all of the stock is absorbed and the rice is cooked through but still has a nice bite to it. The whole process should take about 20 minutes.
Once the rice is cooked, stir in the shrimp and edamame and let the heat of the rice gently cook the shrimp. Once the shrimp have turned opaque, stir in the miso paste. Beyond this point, do not let the risotto boil; miso tastes bitter if it boils. Check the seasoning and adjust the salt as needed. Add the mirin, lemon zest and juice and scallion greens and gently fold in the crabmeat.