Changing advisors within the same department
I'd say try to be up-front about what you're contemplating with both professors, beginning with the current advisor. Unless your current advisor is new to the position, he'll be well aware that sometimes people just don't "click" as you might expect. If you can do some work with the second professor, you should be able to get a better feel for how you two mesh. Definitely be respectful in communications and make an effort to finish anything your current advisor expects you to finish before transitioning. I'd probably also ask up-front about your concerns of funding to make sure you've got the information to make an informed decision.