There are a number of Proxy services that can facilitate what you're looking to do - many free, and some paid. Here's the big problem that I have, and you hit the nail on the head when you confirmed with a Proxy Setting - using a proxy you are basically taking that users IP number and leaves that user responsible for actions.
Too many times (as a hosting company) we see people trying to setup hosting accounts from proxy services. This would be an easy way to gather a number of IPs from various parts of the country to use in later phising or fraud scams. Again, I'm not saying that this is what you're doing (you clearly state what you're doing is NOT illegal), but from a system admin's perspective, it leaves a lot of exposure.
I did a quick search in google for "Anonymous proxy Thailand" and also for "anonymous surf thailand" and came up with a number of different sites that service that country. One particular article which may be of help to you is:
http://www.anonymous-proxies.org/200...and-proxy.html
Strangely enough, I have a friend that travels from England to Thailand about every 2 or 3 months and she also has a hosting account with us, so we have discussed this particular issue many times with various sites being blocked by the Ministers etc. Thankfully none of her hosted sites are blocked for her, but there is a lot of things that can be blocked as part of their censorship efforts.
I'll see if she can offer any other potential solutions that she uses and pass them along to you.