Should I cite a really bad research paper published in my small research area?
Yes you should cite it because:


You know about that paper
You read it in the context of preparing your work. Finding gaps and flaws in previous works is a major part of designing and refining your own research 
By your own judgement it’s highly relevant.


Explain your rebuttal of their claims or method using proper scientific arguments. If I were you I would refrain from using words like “hand waving” or “cranks” in a scientific context.

Whether or not you are the first to discover something isn’t really something you can control. It’s possible that they actually did find something of value but were bad at communicating it. From what you say there seem to be still time for you to be the first to get it right but you won’t achieve that by ignoring previous work.