I believe you should always expect a storm; "be prepared" a boy scout motto; and preparing for "Murphy's law"; the longer the rode, the less strain and wear on the other components in seas and swell. Sure it's a pain dragging in heaps of rope and a heavy piece of chain, but if and when the S hits the fan, at least one aspect is well catered for, and you can concentrate on other worries. My 16 foot dinghy carries 2m of 8mm galv chain on 12mm rode = no worries; my 10 footer carries 3m of 6mm galv chain on 10mm rode = no worries. Try not to anchor near coral bomies and rock shelves. Attach the chain to the anchor head, and through a lesser strength shackle / link to the end of the shaft, so if the anchor is fouled, the less strength link can be broken first, and the anchor retrieved by its head, to be used again.
On the original question, if you can haul up 2m (6 feet) of 8mm chain, and the anchor, go for it, and forget the 6mm chain; if you can't, then you probably won't be able to haul up 6m of 6mm chain and the anchor anyway, if the water is 6m deep. Then get a winch.