WITH HER WRAPAROUND FOREHEAD, tinted shades and knowing laugh, little Lily Shaffer, 5 months, does a killer impression of her papa, Paul, 43. But when he perches heron the piano and sings. "You are my little baby/ You crazy, nutty, little "baby," Lily starts to bawl. "Oh, she doesn't like Daddy's music." he says cuddling her. "She doesn't like that Sinatra thing."

Luckily, Lily isn't always such a harsh critic. In fact, she was instrumental in creating the new version of Dad's opening theme for David Letterman's show. "I was baby-sitting, trying to arrange the music," says Shaffer, relaxing at his home in upstate New York during his and boss Dave's summerlong hiatus, "I put her an, top of the piano and played the theme into her Fisher-Price tape recorder. She seemed to like it."

As Letterman's bandleader for the past 11 years, Shaffer has proved himself something of a human sampling machine, churning out instrumental stump-the-audience snippets of rock classics with his World's Most Dangerous Band—redubbed the CBS Orchestra after a contractual fuss with Letterman's former bosses at NBC. Now, Shaffer and his bandmates have put out The World's Most Dangerous Party, a two-CD collection of rock instrumentals that features cameo appearances by Bill Murray, Martin Short, Letterman and other famous guests. As party host, Shaffer gets to play the smarmy showbiz hack who finds every audience fabulous and every fellow performer mahvelous. "It is done with a sense of irony," says Shaffer, "but I do love the business that I kid."

For Shaffer, a career in showbiz seemed as remote as Thunder Bay, Ont., where he grew up, the only child of lawyer Bernard Shaffer and his wife, Shirley. "Secretly," he says, "I always wanted to go into show business, but it was too far-fetched. We had one channel, CBC, which is why American show business seemed so exotic to me—I almost never got to see it." Late-night rock-and-roll broadcasts from the States eased Shaffer's isolation. "After school I would sit down at the piano, and I would recreate the sound of those records. Really, I'm still doing the same thing today."

A bar-band pianist at 16, Shaffer quit performing to study sociology at the University of Toronto. But shortly after graduation, he landed a gig as music director in a 1972 Toronto production of Godspell. Among the players were future Saturday Night Live stars Gilda Radner and Martin Short, and SCTV's Dave Thomas, Eugene Levy and Andrea Martin. The network of friends eventually led Shaffer to a five-year stint on SNL as pianist and bit player. Shaffer then worked as a session musician—"I loved being one of those studio cats," he says—backing artists as diverse as Diana Ross, Yoko Ono and Robert Plant before signing on as Letter-man's foil in 1982. "David," says Shaffer, "can still make me laugh hysterically at the drop of a hat." For his part, Letterman stated flatly that "I would not be interested in doing the show without Paul."

Offstage, the two are amiable colleagues. "I wouldn't say we hang out incessantly," Shaffer says, "but then, we do hang out every day on TV. It's been a very relaxed relationship through the years."

Shaffer met his wife of three years, Cathy Vasapoli, 37, in the late '70s, when she worked as a booking agent for Good Morning America. "We were always breaking up, gelling back together and breaking up again," he says. "Finally, after a two-year separation, I had to admit she was the girl for me."

As much as he loves domestic life, it's the Biz that still lights Shaffer's fire: "When I met Jack Paar, who's one of my idols, he couldn't get over it—New York magazine had named me as the hippest man in show business. I said, 'You're mad because you feel that you're the hippest man.' Tie said, 'Yes, that's true.'

"I have to admit," adds Shaffer, who knows the title, earned for the jam sessions he has led on Letterman and countless all-star benefits, was awarded half in jest, "that's what I always wanted to be."