i'd try a 165 gr' bullet of either the Hornady Spire Point or Nosler Partition variety. Or the standard Remington Core-Lokt, also in the 165 grain variety. i load imr-4320 with those Remington bullets in my Model 700 in .30-06.........for great accuracy and plenty of power.
you'll get more velocity for hitting whitetails further out; and you'll be able to penetrate a hog's gristle plate, i'd think, out of the 22" barrel of a Handi'.
let us know how you do,
ss'