The 24-year-old Welshman, who competes in the F42 category, managed 16.14m with his penultimate throw against his able-bodied rivals, finishing fifth.
It beat his previous best of 15.93m set at last year's championships.
Davies is aiming to compete in the shot at the Rio Paralympics after his discus event was removed from the competition.
The Bridgend man, who has limited functionality of his right leg with missing bones and no muscle or ligament growth, took gold in the discus at London 2012 and bronze in the shot and is the current European and world champion in both events.
Paralympic champion Aled Davies improved his own shot put world record at the British Indoor Championships in Sheffield.