Can you safely lower CYA without draining your pool?

No. Every “no-drain” solution is either snake oil or risky. Cyanuric acid is chemically stable and doesn’t break down naturally. Products that claim to reduce it are just flocculants that can redissolve, and biological methods are slow and unreliable. Your best bet without draining is reverse osmosis filtration, but it’s not cheap. Otherwise, a partial drain and refill is the only reliable, safe fix.