How (un)safe is it to use an Internetcafe to book a flight online aand in doing so providing your Credit card information ?

Personally I would not use my credit card on a public computer, with modern technology it would not take a genius to copy your details after you have left the cafe and no doubt there will be a trail on the hard drive. Unless there is a computer expert here that can reassure you I would avoid it and look for another method.

Print out the flights you want and then book by phone.

What are your specific concerns? Keystroke recording, web page caching, forms snapshot, visual surveillance, someone peaking over you shoulder? One way to avoid keystroke recording is to place your credit card number in a safe place on the internet, then you can access it, then copy and paste it into the form so no keystrokes are involved. Other than that, it is probably reasonably safe but I would not do it. Even a legitimate purchase can result in your credit card number getting stolen and used. Most credit card companies indemnify the user from fraudulent charges, but sorting it all out can be a pain.

Agree with lopburi3 and consider booking in person. There are as many travel agents in Bangkok as there are internet cafes. In fact they usually co-exist on the same premises! Of course now you have to give your credit card to the travel agent, and probably pay 3% more? Oh well, there's always the airline ticket office, they take credit cards and do not usally charge more.