Cleaning and sanding a greasy handrail for restraining

My handrail has about 30 years of hand grease on it. I've tried a scrub pad with soap and letting it dry before sanding, but it's still not sanding. I just get globs of warm hand grease rubbing loose. It's especially bad in the deep grooves. What's the best way for me to go about this without spending another 3 hours sanding 5 ft of stair rail? The spindles are sanding ok, it's just the handrail part. Thanks!