You cannot define a symbolic spline. At least not in MATLAB. Could you write such a code? Well, yes. But you would need to understand splines well enough to write the code yourself. Functions like spline or even interp1 are not designed to accept symbolic input. Sorry, but they are not, nor do I know of one in MATLAB that can do so. (Could I write it? Certainly yes. But I won't.)
As for what you want to do that you could not do, this we do not really know, only that you did not know how to do what you need to do. Just wanting to do many interpolations is not that hard, so your real problem may just be in how to structure your code to be efficient. We don't know what the real issue is, only what you think to be the issue.