Shanahan Jr. will follow former offensive line coach Phil Trautwein to Gainesville.
Veidt previously worked with Matt Campbell at Toledo and Iowa State.
Unlike last season, Penn State men's hockey finds themselves in strong position for the postseason at the start of January.
Malloe coached alongside new defensive coordinator D'Anton Lynn at UCLA in 2023.
Fink recovered from his upper body injury earlier in the season to excel out in Switzerland.
The Nittany Lions picked up one of their best wins of the season to improve to 18-1.