I had a bearing seize on a King bottom bracket and had to regrease it. It’s not that difficult. Soaking a headset in solvent may be a bit more challenging if you can’t remove the cup from the frame but not impossible. If you have the tools, I’d just pop it out of the frame and soak it. If you can’t take it out of the frame, I’d probably just flow mineral spirits over it with a squirt bottle until the bearings are clean, then fill it with grease.