In the two articles he has written, he questions the Department of Health's policies regarding re-admitting elderly patients from hospitals back into care homes.
But Hawkes is far more outspoken on social media, where posts regarding what he would like to do to Mr Swann were still viewable at time of going to press.
In one addressed to the former UUP leader, Hawkes writes: "Cards on the table. If you attempt to obstruct the long standing liberties of my family, I will cut off either your b******s or your head.
"If I have enough time, I will provide you with a choice. If I do not have such time, I will cut off your head."
In another he says: "There's no justification, no justification whatever, to imprison me or my family within our residence.
"I understand that a lot of people are fearful, but you have no jurisdiction over my or my family's liberties. If you profess such domain, I will extinguish your life."
He frequently uses foul language to refer to Mr Swann, at times describing him as a "little p***k" and a "f*****g idiot".
Hawkes also claims that he contacted the PSNI earlier this year regarding a scheme to prevent the deaths of older people in care homes.
His plan involves the installation of ventilation equipment in "big holes in the walls", with staff to "live on site (bribed with the best family holidays one could ever imagine)".
In other posts Hawkes says the coronavirus "pandemic was over in June" and accuses governments around the world of using case numbers to frighten people.
He also unloads on the local media for "terrorising" the population.
"A heartfelt plea to the NI media - please stop terrorising elderly and vulnerable people due to Covid-19," he says.
"The incessant focus on case numbers is an absolute 'nothingburger'.
"The epidemic is over. Sars-CoV-2 is now endemic and is no longer causing significant levels of disease."
Steve Aiken, the leader of the Ulster Unionist Party, condemned all threats made to his party's minister.
He said: "He [Mr Swann] took on a job which no one else wanted and he has committed long days and nights making difficult decisions, working with his colleagues in the Department of Health and the NHS, to protect the public during a global pandemic, the likes of which we haven't faced in 100 years.
"He has been verbally attacked, threats of physical violence made against him and his family, and attempts made to undermine his good character."