Reskilling?
Not necessary. Anybody who has used continuous integration/deployment and some level of automation or configuration management in the past is vastly overqualified for the majority of DevOps positions already. Middle management loves this new buzzword (along with the tearing down of silos [shrinking head count to you and me], becoming agile [sc(r)um!] and doing everything on demand [sold on the idea that cloud is cheaper - though it very rarely is]), but they don't see that there's absolutely nothing new to it, and can't conclusively explain what DevOps means to them anyway. It is even worse than "Cloud" ever was, as far as clear definitions go.
The only reskilling required is brushing up on bullshit bingo and developing a thick enough skin to carry on with business as usual until this hype is replaced by the next big buzzword.
I'm working for a rather large player at the moment, who fell for DevOps and Cloud approx 3 years ago (because cheaper, on demand, blah blah).
Until then, they had infrastructure in a proper data centre, no single points of failure, excellent performance, and most importantly total control over every bit of it.
The the C-level gang demanded a "lift & shift" to the cloud, asap, ignoring all advice that nothing can be put there as is and expected to work the same way. So what's the situation now?
* automated deployment is only semi-automated and regularly fails, because developers are out of their depth doing "infrastructure as code"
* nothing scales, because none of the applications are designed for it
* hardly anything even fails over gracefully
* monitoring is barely good enough to work out retrospectively what might have happened; usually after customers started shouting
* single points of failure all around because they decided they could do without system and infrastucture guys during the transition from in-house to cloud... because that's what the cloud does in some sort of magic way, right?
* sites regularly topple over, because nobody has thought of testing and benchmarking playing a major role in a disaster-free automated deployment process
* team is approximately double the size than it used to be
* it's vastly more expensive than before
* security was not even an afterthought... and now suddenly becomes a big issue and a rather interesting retrofit; infrastructure guys and sysadmins could have sorted out most of it before the migration, but they weren't needed, because "infrastructure as code". Thing is, if you don't understand infrastructure, you cannot code it. And security begins with properly designed infrastructure.
Bottom line: Developers shouldn't (and usually don't want to) do Ops stuff. Ops guys shouldn't (and usually don't want to) do Dev stuff. And management shouldn't try to "streamline" and "synergise" shit and try to "remove silos" where there used to be excellent communication between teams *before* management started waving the DevOps flag and confusing the hell out of most people, especially those who have been working in either development or ops for more than a handful of years and therefore struggle to see the novelty.