A national Republican strategist said yesterday GOP hopes of winning 1986 gubernatorial elections were enhanced Friday when Wyoming's Democratic incumbent filed for bankruptcy and a Democratic contender in Arizona withdrew.

Popular three-term Wyoming Gov. Ed Herschler filed for bankruptcy, listing $7.5 million in assets and $9.4 million in debts. The bills stem from his part-ownership of the 18,500-acre Yellowstone Ranch, which lost $1.5 million in 1981 in an unsuccessful cattle deal.

In Arizona, meanwhile, multimillionaire Bill Schulz, who almost upset Sen. Barry Goldwater (R-Ariz.) in the 1980 U.S. Senate race and had been the leading Democratic candidate to replace Gov. Bruce Babbitt (D), dropped out because one of his daughters is seriously ill.

"We always thought we would have exceptional prospects in both those states," said Michele Davis, executive director of the Republican Governors Association. "We've got the jump now on money, time and organization in both states. Democrats are going to be scrambling hard to catch up."

Democratic Governors' Association director Chuck Dolan said, however, that many Wyoming voters might empathize with Herschler if he decides to seek reelection.

"I don't know that a person going bankrupt because of farming difficulties in the state of Wyoming is going to get hurt," Dolan said.

Of Schulz's withdrawal, Dolan said: "Obviously, it would have been great to have him in there. But it doesn't make it a race where we are in trouble."