Not without cost.

Back in 1988, I visited Lockheed's plant in Sunnydale, CA where they were building the Hubble Space Telescope. The Hubble was supposed to be launched in 1996 but was delayed until 1990 due in large part to the Challenger accident. That delay added many million dollars to the cost because it had to be kept in a climate controlled clean room. The day I saw the Hubble, there were several people working on it, suggesting there were some substancial labor costs associated with the delay. Despite the delay, they still launched it with defective mirrors.

Launching the Hubble was much simplier than Cassini. Since Cassini was too large to directly launch to Saturn on any existing booster, it had to perform several planetary flybys (2 of Venus, 1 of the Earth, and Jupiter). That's why it took so many years to reach Saturn. During those years, substancial costs were incurred due to the need to keep the ground crew together plus extra DSN range support costs.

Had they delayed Cassini's launch, then odds are the required trajectory would've been even more complicated. There are factors like the relative positions of Jupiter and Saturn that can't be handwaived away. If they had delayed the launch, then the Jupiter flyby would've had to be different to account for the changed positions between the planets. They might've had to fly closer to Jupiter in order to get the required change in velocity and trajectory, which could've exposed Cassini to greater risk. Or, they might've had to pass at a higher altitude, leading to a lower velocity and considerably longer flight time. The cost of the longer flight time, added to the cost of the extra ground support time, would've added many million dollars to the mission costs for no good reason other than to appease some Luddites. It would've been a stupid decision.