ETA: Ninja’d by jz78817!
Buy a better LED bulb—look for those advertised as having a high color rendering index (CRI).
Joey P makes a great point. To expand on it a bit, you might consider not just the labeled color temperature (e.g., 2700K) but also the emitted spectrum of the bulb in question.
(Note: the plots in the link are objectively terrible—axes lack units and scale or are unlabeled altogether. They’re OK on a qualitative level, though).
The OP notes correctly that the sun’s emission spectrum includes almost all of the colors humans can see, which only makes sense—humans evolved on an earth lit by sunlight. The sun’s emitted spectrum is broad (to humans) and mostly continuous. Sunlight’s intensity peaks somewhere between yellow and green, but it slopes down fairly smoothly on either side as you get closer to red and blue, respectively.
But lightbulbs are different. Both LEDs and fluorescent bulbs tend to have much spikier emissions spectra than the sun or incandescent bulbs. Their intensity isn’t smoothly distributed across the color spectrum, but rather made up of several peaks—a 2700K CFL typically has a big, narrow red peak, a few biggish-and-narrow yellow and green peaks, and a smaller-but-narrow blue peak.
That’s a big part of why replacing so many people were disappointed with early CFLs: the light quality from a 2700K CFL is terrible compared to the light from an incandescent bulb of the same color temperature. In isolation, our brains make the light both look white, but when both bulbs are lit in the same room at the same time, the difference in light quality is hard to miss.
Because LEDs tend to have a tall, narrow intensity spike in the blue range and not very much intensity in the red range, people whose veins and bruises look blue in sunlight can expect to see that effect magnified under an LED.
Because our brains tend to adjust the colors we perceive on the fly, the bluer LED-lit veins don’t look a lot bluer—but they do have more contrast against white skin, as would bruises. Since contrast tends to catch the human eye, I suspect that explains why your bruises are more noticeable under an LED.
The CRI of LEDs has come a long way in the past decade or two, and high-CRI LEDs are are significantly better than modern-but-pedestrian models. If you decide to try a high-CRI LED, I’d love to know whether your bruises are less visible than under your existing LEDs.
