Walter emotes, genuinely, throughout the show. He becomes more ruthless and cold-blooded as it concludes, but his traits aren't psychopathic, I don't think. He has good, old-fashioned bouts of rage and vengeance and compartmentalises his double-life well after years of struggling to get the balance right whilst having numerous nervy moments and near misses he was fearful during, he also has to learn how to lie and deceive; it's not second nature to him. I think it's fair to say he tipped too far in the other direction towards the end, but I think anyone in that line of work can be 'turned' eventually.
If he were psychopathic he'd use people more frequently and coldly (automatically) than he does, too, I think.
This is all in my non-expert opinion, of course.
From what I've read, psychopaths basically act their way through life, masking their truer nature and intent or revealing it to like-minded individuals, whilst sociopaths can selectively turn the dial down without much fuss, can form genuine bonds and friendships that they can drop at the flip of a switch. If White were to be any of the two, it would be the latter, but I don't think he's that either, tbh.