@Martin ********
Thailand doesn't recognise different cc categories, there is no up to 125cc here, you either have a full motorbike licence or you don't have a motorbike licence at all. Also you won't have the motorbike stamp in your IDP unless you have a full motorbike licence.
Everybody knows how insurance companies love to pay out and they will do whatever they can to avoid it, this has caught many people out in the past as the insurance company won't pay out if you are not correctly licensed.