How to avoid overly extensive introduction of otherwise unnecessary preliminaries for a minor result?
An appendix, if allowed by your university style/guidelines (and it usually is), is the best option. It strikes a balance between two legitimate concerns:


you want your thesis to be self-contained, and you want to showcase the work you've done (as well as convince others of your work's quality)
in the main text, it may make your message less clear and burden the reader's mind with new notations