No, Safetrade does not involve the use of a credit card and does not need any personal details to work. All items traded are either toribash items, or toricredits, both of which are artificial items that have no direct value in real currency.
Basically, you put in a trade offer, and someone else puts in their counter offer, and you click accept if you wish to accept the counter offer.
Again, no real world Items are used in this process.