The fact of the matter is regardless of how it's spelled, Americans don't say bollocks anywhere near as often as Brits. And even when they do, it's much more likely to be used (and understood) as a low-impact general-purpose profanity, rather than a specific anatomical reference.
I can't find the reference right now, but I'm pretty sure Obama publicly referred to something as being "all bolloxed up" (in disarray) recently. I also believe that Americans are much more likely to use the -xed spellings than Brits (they did pretty much invent sox, after all).
In consequence of the American "sanitisation" and spelling bias, Brits themselves are likely to find written instances of bollox less offensive than bollocks (this also happens with asshole/arsehole).
Related examples of "sanitisation" include berk (Berkeley Hunt = cunt), Father Ted's feck (=fuck), and perhaps Princess Anne's "Naff off!" to obtrusive press photographers.