I've spent quite a few Augusts in the area - have always had enough sunshine to have a good holiday, yeah, got heavy rain some times - but usually short sharp stuff.
Typical is one or two showers/storms per day (can be at night) with sunshine/scattered cloud between. Over about 50 days in total over the years I have had maybe 15 with no rain, 3 with no cloud, and maybe 3 where it rained more often than not (but not continuously - still had some sunny patches, no day was a write off), and maybe a half dozen (some of which coincide with the rainy days) where it was windy enough to make conditions unpleasant on exposed beaches (so go seek somewhere sheltered where it can by real nice - and yeah, it can be real nice on yer bungalow verandah sipping elcheapo local rum listening to the plop-plop or raindrops on the big banana leafs beside you).
I have never struck a patch of prolonged rainy weather like we have just had here in Australia's summer. It can happen in the Andaman, but is nowhere near as common as in the mid-latitudes.
Now I really like Krabi, paticularly Railay and Ton Sai - the one reservation I have these days is that in high season the area can get overcrowded and overpriced. This aint the case in August - and the deals Agoda, travelfish's booking site and the others offer are red hot for real nice accommodation.