Handcuffs and gentle handling is possible, of course, but what about using mere intimidation?
From your questions it seems that we're mostly dealing with common thugs, not some insane revenge-fueled supervillain. Common thugs are very much human.
If your superhero is able to show a display of overwhelming raw power, such as shrugging off any attack the thugs do or bend/crush nearby solid objects, then perhaps the thug would realize that giving up is the best thing they can do in the situation. Having increased speed may help too, to make the idea of escaping all but impossible. "Just give up and nobody needs to get hurt" and all that.
Only once all of that fails would you resort to physical capture, preferably as effortlessly as possible (Swiftly handcuffing them, easily lifting them off the ground as if they're small children, etc) so it would further cement the image of overwhelming power once the story spreads all over media.
In fact, once you've done this often enough, your reputation will probably precede you and your mere presence would be enough to intimidate nearby thugs to turn themselves in.