The recoil will increase because the weight is reduced. The muzzle velocity will be reduced about 30 fps for every inch you take off the barrel. This will begin to significantly affect trajectory at long ranges (beyond 300 yards), but at normal hunting ranges it shouldn't be a problem.
For example, firing a 165 grain Hornady BTSP or Nosler Partition from a Winchester case over 43.5 grains of IMR4895 produces 2700 fps from a 24" barrel and 2550 fps from an 18" barrel. Zeroed at 200 yards, per Cooper's precepts, both will stay in a 4.3" circle to 230 yards. The longer barrel delivers the bullet at about 1870 ft-lbs at that range, while the short one gets it there with about 1650 ft-lbs left. At 300 yards the bullet from the short barrel has dropped 9.4 inches below the 200 yard zero, while the one from the long barrel has dropped 8.4". When zeroed at 200 yards, it takes 300 yards to get the point of impact one inch different between them.
Nick