The double-bladed watermelon knife is not common. In fact, over 99% of all watermelon knives have one edge only. In some parts of the world, this is actually a safety requirement. Therefore, you will have to stick to a single edge. You are less likely to use both edges anyway – unless one of them gets dull and you do not feel like sharpening it.
On the other hand, there are watermelon slicers with double-edged blades.