You might think that the Cleveland String Quartet would have no hesitation about accepting Niccolo' Paganini's personal quartet of Stradivari instruments. But the eminent group did pause when the Corcoran Gallery of Art, which owns the matched set, offered the instruments last year.

"It was nice for us," recalled cellist Paul Katz yesterday, "but it wasn't the kind of thing to make us jump out of our skins. After all, we have our own instruments too." In the past, Katz has played his Guarneri. Violist Atar Arad has an Amati. And first violinist Donald Weilerstein has a Strad of his own.

Arad was less restrained about the Paganini Strad viola. It is the viola to have if you can have only one--the one for which Berlioz, on Paganini's commission, wrote the most famous solo work for viola, "Harold in Italy."

"I will play that Strad from now on," Arad said as the players, including second violinist Peter Salaff, gathered in a Bethesda home, where they are staying while getting ready for a concert at the Corcoran tonight. There the newly reconditioned instruments will be introduced, except for the cello, which is still being repaired.

The instruments were willed to the Corcoran in 1966 by Anna Clarke, whose husband donated one of the gallery's wings. Since then they have led an uncertain existence. The gallery's board ruled out leaving them in storage because they would deteriorate, or "go to sleep," as they say in the trade.

For several years the instruments--although in less than optimum condition--were used occasionally by a quartet of National Symphony players. "But that didn't work well," recalled Corcoran trustee Jane Alper, who made the instruments her project. "The National Symphony players did not play them full time. So finally I suggested to our chairman, David Lloyd Kreeger, that the instruments should go to a major full-time group--just as our Amatis are used by the Tokyo String Quartet. He said, 'Okay, you find them. It took almost a year and a half to get this far.' "

There were several problems. Foremost in the Cleveland players' minds was the condition of the instruments. The Paganini cello, in particular, gave pause.

"I looked at it and I was alarmed," recalled Katz. "If we took the Strads these instruments were going to be under enormous pressure. And there was a spot under the A string on the belly that was slightly pushed in. I took it to a concert in Princeton and played. It sounded wonderful. But here was an instrument of major historic importance. And if its bridge broke through, that would finish it."

After the group decided to accept the instruments on indefinite loan, the cello and the other instruments were taken to master craftsman Rene Morel in New York. "He has somehow worked a reinforced piece of wood right where the foot of the bridge fits," said Katz, "and it's fine."

As a gesture of thanks, the quartet will play three concerts a year in the Corcoran's little Armand Hammer auditorium, just as the Tokyo does.

One subject they won't talk about for quotation is the value of the instruments, because of security. But Katz noted that a Stradivari violin recently went for a million dollars, and laughed when asked if his new cello is insured for less.