Agile; The first supposition to clean the belt is perfectly acceptable but perhaps with warm water, not hot water, and with a mild soap rather than a detergent. Personally. I would avoid silicones like the plague, but that's just me. Of course cleaning the seat-belt fabric will improve its appearance but may not correct the problem of inadequate retraction force. And yes, cleaning the seat-belts can be regarded as normal maintenance.
Your second supposition of sending the whole unit to an automobile seat-belt overhauler for a new belt installation, and a colour of your choice, still may not correct the problem of inadequate retraction force. But it may determine and correct the problem with the inertia reel. From experience I can tell you that the practice of replacing seat-belt fabric this way is more common that you may think, I've done it myself. BUT, insist on a proof-load certificate, or statement, before putting it back into the helicopter.