Yes it's safe. Just remember to ground yourself before touching the parts. Just touch a metal object (the case will do just fine) before touching the hardware.
And you can leave the ram and cpu in the mobo, but I'd disconnect all of the other parts. You don't have to disconnect them, but I think that it's easier to do so.
And remember to put the small copper (I think) thingys under the mobo before putting it in the new case. So that the mobo is resting on the thingys instead of the case. If the mobo touches the case there is a good chance of "bye bye mobo".