I am interested in understanding the generalized Stokes' Theorem. From my understanding, this theorem involves differential forms and exterior algebra, and tensors (to some extent).
I'm not particularly interested in geometry; I do like analysis, though, and generalizations of the fundamental theorem of calculus have fascinated me since I first heard of Green's Theorem.
I've taken vector calculus; I'm in real analysis now, where we are going to cover the change of variables theorem of multiple integrals before we finish. I haven't, however, taken any classes in geometry. The point-set topology of metric spaces is as far as my topology knowledge goes.
With this background, is there a path towards self-studying (and hopefully understanding) Stokes' Theorem?
There is definitely a path towards getting there. In fact, I recommend jumping right into "An Introduction to Manifolds" by Loring W Tu.
The advantage to this book is that, coming from your background, you should find the reference to be self-contained. That is, you should be able to just read through this book without outside references.
There are definitely books that build up to the "Stokes' theorem" punchline faster, but this seems about right for where you are. If you use this book, I recommend skipping chapters 3 and 4 at first, at least to get through to Stokes' theorem.