Sneakylong Hurts relies on his legs more. So his running won't be affected.
That's a perception that can be readily gleaned. However, prior to the shoulder injury, earlier in the season, Hurts' greatest improvement from last season to this has been his arm, mechanics, accuracy, increased ability to read defenses - not being a one-look, tuck it and go kind of 'running QB'. Since the injury, the forced layoff/recovery and then the dynamics stemming from the flow of both playoff games, he's not needed to get back to airing it out. Is the shoulder injury having a limiting effect on that? That's hard to know.
I see Mahomes more of a scrambler to buy time. From the KC games I've watched over the past few years, he's quite adept at improvisation. From what I understand, his high-ankle sprain is allegedly on the mend and shouldn't effect his mobility. If it does, he better get significant support and protection from his O-line.