Police have identified the suspect as 50-year-old Franz Wrousis, a drifter with a criminal record, and warned residents that he could still be armed for attack.
It was not clear what may have prompted the man to assault the two office workers, one of whom was badly hurt. CSS, whose office Wrousis stormed, said he was a client.
Two other customers in the office were treated for shock, while a fifth person was hurt during the police response, the authorities said.
Authorities issued an international arrest warrant for the suspect as the police carried out an intense search.
A spokeswoman for German federal police said that one of their helicopters was being used in the area as part of the manhunt.
"A big part of the canton's border is actually on the German border, so that's why German colleagues are also looking for the guy," a Schaffhausen police spokeswoman said.
CSS offices in Schaffhausen, a quiet medieval town of 36,000 residents, and in other parts of the region remained closed while the manhunt continued, a company spokeswoman said.
"I hope they arrest him soon, as it is a threat for other people, either here or in other cantons. He has to be found and arrested," said local resident Diego Faccani, 52, a clothes and shoe salesman.
A man who identified himself only as Samuel and who lives in the area next to where the suspect's car was found on Monday evening said he had often seen the suspect, whom he described as "very disconnected" and uncommunicative.
"He looked like a schizophrenic, but we didn't think that it would be that bad. We didn't see him as a threat or anything. We didn't think that he was dangerous, but yeah, definitely he was a strange guy," said Samuel, who did not want to give his family name.
"The last time I saw him was on Sunday morning, when I was walking our dog. He was standing still, because he saw me coming or somebody else coming and he didn't move until everybody else was gone again."
Police who put part of the old town of Schaffhausen under lockdown on Monday were no longer combing the wooded area where the suspect was thought to be living and had fanned out across a wider region.
A picture of Franz Wrousis released by the Swiss police
Police with search hounds hunted on Tuesday for a chainsaw-wielding loner who mostly lived in the woods, a day after he stormed into an insurance office in the Swiss town of Schaffhausen and wounded two staff members.
