If your little guy seems to be handling easily, then I wouldn't worry about if it's "too soon" or not. But I would keep the sessions short and infrequent until you get him eating consistently. If he doesn't start eating, you may have to stop handling him altogether until he does.

The easiest way to thaw a mouse is to put it in a baggie and set the baggie in a bowl of hot tap water. You may have to change the water when it cools. Be sure the mouse is completely thawed and heated through. I thaw mine overnight in the fridge and then warm them up in the water when I'm ready to feed.

You can refreeze it once, if you want, but I wouldn't do that more than once.

One last thing...when you're dangling a mouse for your snake...you really should use tongs or something to distance your hand from the prey. You're lucky the snake just climbed up your hand, rather than striking and biting. Your hand is nice and warm and very close to a yummy smelling mouse...very easy for the snake to miss and hit the wrong target.

Sounds like he just wasn't ready to eat yet...or he may not be too sure about the frozen/thawed thing as actual food. Some snakes are skeptical and take some convincing.