I can't speak for AmE, but in BrE, fudge in OP's context has more the sense of...
To reach a makeshift solution by glossing over differences or blurring distinctions
to prevaricate or temporize.
That definition is from OED, who also flag up...
to fudge and mudge [mudge: fanciful rhyming alteration of fudge]
first recorded in a speech on 2 October 1980 by British politician David Owen
Therefore I would say that fudging an issue means distorting/smudging the issue, so it's not clear exactly what is being discussed. That's somewhat different to dodging the issue (actually avoiding addressing it at all, rather than making it confused), and completely different to cheating.
Having said that, there are contexts where if a makeshift solution is fudged/cobbled together, someone might say you were metaphorically "cheating" because you didn't "follow the rules" which were implicitly expected to be observed by your solution.