NHL GMs and Assistant GMs don't need to be "advanced stats guys" per se, insofar as being people with analytic backgrounds ala Chaykha. You can hire people to do the hard analysis for you, it just has to be something you value as GM, and factor heavily into decision making. No different from the various "capologists" that teams hire. Like any executive, a GM will surround themselves with experts in all the important areas of analysis, whether that's player or cap analysis, and it's up to them to allot the proper value to the info they receive.
Take the example of two former players, now GMs: Steve Yzerman and Marc Bergevin. Do I think either guy can delve into statistical analysis the way Rob Vollman or some of the people on this forum can? No, probably not. But I know based on how Tampa conducts business that Yzerman is properly factoring such experts and the work they do, into his decision-making, whereas Bergevin receives a detailed statistical presentation on why trading Subban for Weber is a terrible idea, makes the trade anyway, and fires his analyst afterwards. Then you have Lou Lamoriello and Brendan Shanahan in Toronto, as old school as it gets, running a team that is very clearly prioritizing advanced statistical analysis.
So this whole notion about GMs needing to be non-players is bogus. It's an argument that I'm sure owners love because some of them are starting to replace expensive hockey people GMs with analytics guys because hey, analytics guys make presentations and generally work for peanuts, but in reality these people are better off being experts and advisers that are hired by GMs with experience navigating the hockey world at all levels, who have to do more than look at stats. There's talent relations, player evaluation, culture building, hiring and firing, deal-making, etc. GMs have to be good at everything, including the politicking that comes with any management level job.