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.

Ildar Dadin is serving two and a half years for a series of street protests.
He told his lawyer that he had been strung up by his handcuffed wrists, had his head shoved down a toilet and been threatened with rape and death.
Russia's prison service says the claims are untrue but will investigate if the activist complains formally.
Unusually, the allegations made the headlines on state-controlled television on Tuesday after Kremlin spokesman Dmitry Peskov told reporters that the case merited "the closest attention" and that President Vladimir Putin would be informed.
Dadin's supporters gathered outside the justice ministry on Tuesday evening in protest.
Ildar Dadin, 34, says his problems began after he was transferred to Prison Number Seven in the Karelia region of north-western Russia in mid-September and sent directly to a punishment cell.
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Now out of isolation, Dadin has dictated a letter to his wife via his lawyer, in which he says he was beaten and kicked repeatedly by up to a dozen prison staff.
One day, he alleges, he was hung from his wrists for about half an hour causing "extreme pain".
"They then took off my pants and said that they would bring in another prisoner who would rape me if I didn't agree to end my hunger strike," Ildar Dadin writes.
He had stopped eating in protest at being held in a punishment cell.
Russia's FSIN prison service told the BBC that Mr Dadin was put in isolation for what a spokeswoman called "violations of the detention regime", but insisted that his claims of beating and torture were false.
"There's no way illegal methods were used, especially for such a well-known character," Kristina Belousova told the BBC by telephone.
"It's not the first time we've seen this, by people trying to attract maximum attention," the spokeswoman added.
Ildar Dadin was sentenced in December 2015, under Article 212.1 - a controversial law that makes repeat violations of Russia's strict laws on street protests a criminal offence.
"We didn't expect this to happen. It's awful," lawyer Alexei Liptser told the BBC, after visiting his client on Monday and transcribing his account.
"He is frightened and subdued," the lawyer added.
As the allegations of abuse spread on social media, and reached the Kremlin, Russia's human rights ombudswoman ordered a regional representative to visit the prison and said she was taking the case under her "personal control".
In a dramatic conclusion to his letter, Ildar Dadin tells his wife "I am not afraid of dying. I'm most afraid of not being able to tolerate the torture."
Paralympic champion Aled Davies improved his own shot put world record at the British Indoor Championships in Sheffield.
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Russian officials are investigating claims that a well-known opposition activist has been repeatedly beaten and threatened in prison.