My condo in Bangkok is around 10 yrs old now and the doors under the kitchen sink are starting to rot away around the corners but apart from the doors the rest of the cabinet structure is fine.

How do I replace these doors? Do I take them out and find some furniture place that will cut replicas? Im not a big handyman so any advice appreciated.

Normally there are workers available that can come and make for you - maid grapevine can be useful - often other have done and they or there maids will have taken contact information and can provide reference of there ability. That said am sure some of the custom furniture shops would do for you - but they can be expensive.

Good idea I will ask the maids and there are a few full time handy men floating around so they should know as well