Kawthoung is definately not a shoppers Paradise. But there is some shopping to be done there.
There are no real shopping streets, or shopping areas because not only is Kawthoung only really a fishing town, it is also quite a small town too.
The best way to shop is to just meander through the streets and look inside alot ofthe Corrugated Iron Erections with open doors, you will find most of them are shops. They sell a multitude of different things. However also keep in mind that Kawthoung is a crossing point for travellers, and so prices are not so cheap. I would say most wares are more expensive than Thailand, You'll be charged in Baht.
What to buy: I saw for sale many wooden crafts; sculptures, carvings and teak boxes etc. Alot of basketry and lots of local Leather goods. Which were quite nice quality.
Also Sarongs are plentiful, and also Longhi (the checked/plaid sarongs that Subcontinental men wear). I definately bought some of these. Also some leather ware. I hummed and Harred over some of the beautiful wooden crafts, because most of the goods were fashioned from aromatic teak wood. teak is becoming very very rare, and it is not good to encourage teak loggers with foreign demand.
What to pay: 400 - 40,000 baht. ($10 - $1000 US)
What to buy:
These burmese cigars look like a jumbo version of the indian "bidis". A rolled leave with crushed leaves inside and a carton filter; I guess it is tobacco, but I'm not so sure about it (it is no drug, anyway).
They are greenish in colour and they are quite strong. They are ridicously cheap, especially at the stalls in the port area.
There are a few local shops on the main street going from the port to the hill. You can buy very nice sarongs and other tissues at very good prices. Many Burmese sarongs have a blue/cyan squares design, that is much different from the Thai or Indonesian ones. Most other goods on sale are chinese.