With all due respect, securing an anchor is not a job for cords, bungees and ny-straps. The loads in a rough seaway are too much, and the potential problems of a loose anchor are too catastrophic. Something as simple as a snubber with chain hook attached to the shackle and tensioned to a cleat in the anchor locker or on deck will do. If you have proper ground tackle you should have a section of chain attached to your anchor in which case you can use a
chain tensioner. An elegant, secure method that works with one hand.
Windlasses fail, or are inadvertently activated, so they are not a foolproof method for securing the anchor.
Whatever the solution you need to be able to deploy your ground tackle very quickly. Emergency scenarios like engine failures while navigating your marina approaches, or sail and running rigging failures approaching a lee shore are both high drama and split second situations. You and your crew need to be able to release your ground tackle in very short order, and probably on a pitching deck in adverse conditions with your hair on fire. Think of your anchor and ground tackle as your emergency brake - you don’t want to have 4 handles and a button to make it work. And you don’t want 30 to 60 lbs of iron going weightless on the foredeck while you are occupied with bringing the boat under control.