Soaking the tortoise is good. Going outside into a large proper secure enclosure during fair weather is excellent. Going outside to run around loose in the yard, is not a good idea.
With the questions you are asking about interaction with your tortoise, a greek or pancake would not be my first recommendation. Both species have a general reputation for shyness in comparison to others.
Not to worry, my tort will be in an enclosure when outside and supervised by me. That's interesting you say that Greeks tend to be shy, I've heard quite the opposite! Which species tend to be more outgoing and friendly?