I’ve seen the expression being used quite a lot in non-English speaking countries by recruiters themselves and I find it a bit odd. Have they chosen the wrong way to be cool?
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For a job recruiter, the term 'headhunter' is only slightly derogatory. One might consider using it to the person's face but it might feel a bit strange by connection with the other original meaning. A recruiter is probably very aware of this term and has probably been inured to it through over-use. The dictionary will not say it it is derogatory because it is not taboo enough, but it does have a slight connotation of negativity ('garbage man' is not derogatory but other terms like 'refuse collector' or 'waste management personnel' might be favored.
Disclaimer: I have no data or reference to support this answer other than inner reflection. I'm not sure exactly how to support such claims of nuance other than by bald statement.
It's certainly not derogatory towards the people whose heads are being hunted. In the usual modern sense of the word, headhunters are typically executive search firms that recruit skilled professionals for jobs that usually offer competitive or superior pay and benefits. The analogy with primitive hunters who collect human heads as trophies is, when separated from the significant disadvantages of actually being killed and decapitated, rather flattering for the quarry: to be headhunted is to have a head worth hunting, after all.
The earliest citation in the OED is from a 1961 issue of Fortune magazine: "McCulloch had no compunction about using these executive recruiting firms. They were, he knew, often derisively called ‘body snatchers’, ‘head hunters’, ‘flesh peddlers’, and ‘pirates’." I wish there were more context, but my guess would be that these were considered terms of derision by employers who didn't appreciate having their best employees poached away from them, rather than by the firms' customers or the candidates they recruited.
It's worth noting that the OED definition itself ("orig. U.S., an employment agent or agency specializing in the recruitment of managers and other skilled personnel by identifying and approaching preferred candidates; one who recruits using these methods") doesn't say anything about it being considered a derogatory term today.
edit: You reference this link, which makes the analogy with real estate agents who prefer to be called realtors or real estate salespeople. I don't think that's the best analogy ("Realtors" is a trademark of the National Association of Realtors, and nonmembers aren't supposed to use it), but we might also consider an individual who wishes to be called a sanitation engineer, but whom everyone else would simply call a garbage collector. In all three cases, the situation involves the subjects preferring an overtly positive term over a term that most disinterested observers would probably consider neutral at worst. I would differentiate between that and a term that is actually derogatory, though some may disagree.