Cadabra does not need Conda (I am not using Conda myself either). A standard build from source will produce a Jupyter kernel which runs with the Python installation which is picked up at build time.
Your main problem will be that you are trying to do this on Windows 10. Building Cadabra from source on that platform is far from trivial, and I have no idea how to do that such that it builds against the version of Python shipped with SageMath. In addition, SageMath is a bit of a weird beast to start with, as it tends to ship with everything it needs, including compilers. That is only changing slowly recently, but I am not following this very closely.
Your best bet, if you insist on staying with Windows, may be to ask people on the SageMath mailing list how to build a mixed C++/Python program like Cadabra from source. A better choice may be to switch to Linux, as that platform really is much more friendly for software like this.
Feel free to get in touch wagain ith more technical questions if you decide to give this a shot.