Sen. Orrin G. Hatch (R-Utah) said yesterday that Secretary of Labor Raymond J. Donovan is apparently "going to hang tough" in his Cabinet post. Hatch guessed that the federal investigation of Donovan's business activities might not be concluded until August.

The work facing special prosecutor Leon Silverman, who is in charge of the special inquiry, "keeps piling up," Hatch told a reporter.

Hatch, chairman of the Senate Labor Committee, said that Donovan, meanwhile, continues to indicate "through his people, that the things being said about him are wrong."

"I think he's going to hang tough," Hatch said, "and I don't blame him. Other than the investigation of our committee, he acts just like an innocent man should act."

Hatch was referring to the hiring of private investigators by Donovan's New Jersey construction company to investigate Hatch's committee for its role in pressing the Donovan investigation.

Newhouse News Service reported yesterday that one of the detectives is Robert L. Shortley, 60, president of Interspec, a Washington-based company. He told Newhouse that he had been hired by Donovan's firm, Schiavone Construction Co. of Secaucus, N.J., five or six weeks ago to be Schiavone's "eyes and ears" in the nation's capital.

In June, 1980, Shortley was one of the detectives hired in the celebrated Republican musical wires caper which centered on suspicions that someone had planted a bug in the Capitol Hill offices of Republican national co-chairman Mary Crisp.

Metropolitan police who finally entered the case wound up charging Shortley and three other private investigators involved in the case with operating without licenses.

The police also concluded, after a seven-month investigation that embarrassed all concerned, that the suspicious wire that caused all the fuss was the innocent remnant of an interoffice bell system.

Shortley, a former FBI agent, was quoted by Newhouse as saying that the charge against him was withdrawn after he challenged it, but that he has since obtained a license. Under District law, private investigators must undergo a police security check and pay an annual licensing fee of $158.

In his work for Schiavone, Shortley told Newhouse, "I don't put on wiretaps and I don't secretly record conversations. I do my work in a very low-key way."

In a letter to Senate leaders, Hatch and the committee's ranking minority member, Sen. Edward M. Kennedy (D-Mass.), denounced the private investigation as "an affront" to the Senate and asked for advice on a formal response.

Shortley said he felt Schiavone was "under attack" and had a constitutional right to defend itself.

Donovan still owns a substantial interest in Schiavone Construction, but he has denied through a spokesman that he ratified the controversial detective hiring.

However, Hatch has said Donovan told him of it a couple of months ago. Hatch said he thought Donovan was just "popping off" at the time.

The Senate committee's latest role in the investigation involved its referral to special prosecutor Silverman of a former business associate, James J. Donelan, who testified this week that he used to have lengthy conversations with Donovan about bid-rigging on New Jersey Turnpike Authority projects.

Donelan said Donovan told him he was able to get inside information from the Turnpike Authority's longtime executive director, William Flanagan. Flanagan has denied such allegations as "patently ridiculous."

One of Schiavone's lawyers, Theodore Geiser of Newark, meanwhile, told United Press International that Donelan's lawyer, Arnold Gold, had asked Schiavone Construction on Jan. 16, 1981, for $10,000 from what Gold described as a separate account set up for Donelan in early 1970s. Geiser said no such account existed, but that a week later, the FBI interviewed Donelan.