I got that diagnosis (high cholesterol) about 10 years ago. I decided to instead try going on a plant-based diet for a few years. That pretty quickly took my bad cholesterol level away down. I've been on a vegetarian diet now (that's pretty heavy on fairly) for several years, and even though my cholesterol level has gone up a bit, it's still not that close to where it was before.
This situation won't work for everyone, for various reasons. But from my experience it's been a feasible alternative, at least in the mid-term. So I thought I'd mention it.