Inside this small and vexed question even smaller questions are struggling to get out. 

The most detailed discussion to date appears to be 

Alfredo R. Paloyo. 2011.  When did we begin to spell “heteros*edasticity” correctly? _Ruhr Economic Papers_ 0300. 
[see here][1]

(a reference I owe to @Andy here in Ten fold chat). I can't do justice to its dense and detailed discussion. What follows is more by nature of an executive summary, modulo a little whimsy. 

Modern search facilities make it possible to be confident that _homoscedastic(ity)_ and _heteroscedastic(ity)_ are modern coinages introduced, explicitly or implicitly, by the British statistician Karl Pearson in 1905. (Pearson ranged widely over several disciplines, but in the second half of his life his work was firmly centred on statistics.) 

Modifying _c_ to _k_ raises absolutely no statistical issue. The idea is at its simplest that the Greek root being used includes the letter kappa ($\kappa$), whose direct equivalent in English is _k_, and so that _k_ is the correct spelling. 

However, as others have done elsewhere, we note that this suggestion was made particularly by J.H. McCulloch in the journal _Econometrica_, a journal which failed to follow the same logic by renaming itself _Econometrika_, nay _Ekonometrika_. (The roots behind "economics" are also Greek, including the word _oikos_. Ecologists will want to add that there is a journal _Oikos_ even though, once again, ecology did not call itself _oikology_.)   

Further, it is remarkable that Karl Pearson was no hater of _k_, as he changed his own name from Carl to Karl and named his own journal _Biometrika_, in full and conscious recognition of the original Greek words he used when devising that name. 

The root question then is purely one of language, and of how faithful it is proper to be to the original words behind a coinage. If you follow up the McCulloch reference, the discussion turns to whether such words came into English directly or via other languages, and so hinges on criteria that may appear to many readers as arbitrary if not arcane. (Note that _criteria_ is another word of Greek origin that escaped the _k_ treatment.) Most language authorities now acknowledge that present spelling can owe much to historical accidents and that any long-established usage eventually can trump logic (or more precisely etymology). In total, there is plenty of scope here for scepticism (or skepticism). 

In terms of tribal or other preferences, it is my impression that 

1. Econometric usage seems to be shifting towards the _k_ form. The McCulloch paper had an effect, indirectly if not directly. 

2. British English seems to make more use of _c_ forms over _k_ forms than does American English. The form _sceptic_ is standard in British spelling, for example. 

All puns and wordplay here should be considered intentional even when accidental. 

  [1]: http://www.rwi-essen.de/media/content/pages/publikationen/ruhr-economic-papers/REP_11_300.pdf