Brunskill claimed the trophies for top scorer and website player of the season while Charlton took the most voted from players and supporters.
Both netted on Saturday in Town's crucial 4-0 win over fellow strugglers Ilkeston, which helped secure top flight survival.
Joint boss Phil Brumwell paid tribute to the pair.
"Danny's record is unbelievable, that's why we turned down a big money offer from Gateshead," he said.
"There are not too many players who can guarantee 20 goals a season and he knows he can improve.
"Karl has been consistent and has played more or less every game, even at left back, but when we put him further upfield he's scored goals and looked dangerous.
"It's a shame we couldn't use him up there more often because we lacked a natural left-sided player with Alex Janes out."
As well as the two award-winners, Brumwell also sang the praises of centre back Richard Forster for his composure and experience at the back, and ex-Town boss Lee Nogan, who quit as manager in October but came back as a player to help out for the last few games.
"Lee didn't want to see Whitby go down and you've got to take your hat off to him," added Brumwell.