Surfing and skimboarding are different. So, it is impossible to surf with a skimboard.
In terms of the board size, a skimboard tends to be smaller than a surfboard. When skimboarding, the person runs towards the wave. He/she drops the board onto the sand and jump when the wave comes.
Unlike skimboarding, surfing is much more dangerous. The person often chooses to surf in deeper water and play with large waves. So, the small size of a skimboard is not safe enough to keep players balanced on the strong large waves.