You can't do it the way you say, the same way you can note redefine the exponential function and expect that everything else uses your new definition. Christoffel has a unique definition. That definition is used in several places. If you post your problem or an example that illustrates what you need more specifically, then one could imagine a solution.
Meantime, what you can do is ignore entirely that all these tensors exist predefined according to textbook definitions (Christoffel, Ricci and Riemann) and define yours, say C, R, Ri, where your C I imagine is in terms of the metric g and its derivatives, R is some contraction of Ri and Ri is a function of C, g and its derivatives. To define a W traceless tensor related to Ri is also trivial. All that can be done defining tensors as explained in the Physics,Tensors help page, the sections on how to define tensors. Actually, it wouldn't take more than 5 minutes to define three or four tensors like those.
To summarize, you can always ignore the existing definition of these tensors and work with an entire set of other ones that you define with ease in a few minutes at most. It is simpler if you could show, on a Maple worksheet, more specifically, what you need and how do you intend to use it. There may be other more convenient solutions.
Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft.