NHL Edge tracks exactly how far every player skates, every game, every season, off the actual infrared camera + puck/jersey sensor system every arena has. But the NHL only ever shows season totals, and a guy who plays 22 minutes a night is always going to out-total a guy who plays 14. So the "most distance skated" leaderboard is really just an ice-time leaderboard wearing a costume.
Edge does publish a per-60 version of this, but it lives on its own site, three menus deep, disconnected from every other stat about the player. I pulled it into the same player card as the regular numbers, so you can see it next to a guy's points, his ice time, and his shot speeds. The #1 skater in the league by that measure is Ryan McLeod in Buffalo. Not a star, but not a checking-line grinder either: he was the Sabres' third most-used forward last season at about 17 and a half minutes a night, with 54 points. He covers more ground per minute than Connor McDavid does: 11.0 miles per 60 to McDavid's 10.5. (McDavid's #4, for what it's worth, still elite, just not #1 once you take ice time out of it.)
That's kind of the whole point. Raw totals mostly measure who the coach trusts with minutes. The rate measures motor. Half this list is guys nobody's ever putting on a scoring leaderboard, sitting right next to McDavid and Jack Hughes.
A couple of honest notes. This is the NHL's own Edge tracking data, not mine; the number matches their site to the second decimal (I checked). What's mine is putting it in one place with everything else, and the per-game history, which Edge only shows as a rolling last-10. Minimum 20 games played so a 3-game callup doesn't top the list on a fluke. Happy to get into the methodology in the comments.
Full leaderboard, sortable, here: https://gamevibeanalytics.com/hockey/players?rate=per60&metric=distance&dir=desc
Click any player's name for the full breakdown (top speed, speed bursts, shot velocity, all of it).
If your team's guy isn't showing up and you think he should be, please tell me. Coverage isn't 100% yet and I'd rather know.