My experience/opinion is not to turn the Physics course into a Math course. In practice, that means teaching the algebra-based course using *at most* basic trigonometry and quadratic equations. For the calculus-based course, I would limit the math to simple derivatives and integrals, but keep the general level of the course at algebra. I don't have the students do any derivations on exams, and I provided them with a formula sheet last year.
But realize, this decision is up to you- just make sure you communicate to the students on the first day what your expectations are, what they should know, and what they can do if they don't. For example, you may want to quickly solve a simple kinematics problem using calculus for the class, and tell them they are responsible for being able to work at that level if they want an 'A'.
Enjoy the experience!