Light is made up of photons, which carry momentum. When light hits an object, that momentum can give the object a push. Rather than carry its own fuel, the LightSail is pushed by sunlight to accelerate. The same principle could be used with our speed skater and, say, a laser pointer. Blue light is among the most energetic of visible wavelengths, so using a suit that reflects that color and a corresponding laser to aim at it, we can get the best results.
The momentum of a single photon is given by
where h is Planck's constant and λ is the wavelength. Blue light has a wavelength around 420 nm, which gives a momentum of 1.58 x 10^-27 kg m/s. Since we're bouncing the photons off the skater, we actually get twice the momentum compared to absorbing them. To figure out how many photons we need, we have to find the minimum velocity boost that will give an advantage.
In 2018, the men's speed skating medals were decided by 2 milliseconds over a 5000 meter course! The difference in average velocity was 7.24 x 10^-5 m/s. To get the momentum, we need a mass for the skaters, which this page suggests is around 161 pounds. Comparing that to our per-photon momentum shows we need a total of 1.6 x 10^24 photons to make a difference. The energy in each of those photons is simply the momentum multiplied by the speed of light, so the total energy required is 790 kJ. Delivering that over the 6-minute race time gives 2.1 kilowatts. This is what a 2-kilowatt laser looks like: