> I assume there's some fatal flaw to this

It would take massive expenditure of energy to create and preposition all of those nukes.

A direct contact blast (as in Project Orion) would obliterate a thin radiation sail. Radiation effects might impart a propulsive force to a more distant sail, but probably not enough to generate the sustained acceleration required. Pulsed acceleration blasts would dynamically disrupt the ultralightweight sail rigging (compared with a continuous gentle pressure from the sun or a launch laser). EMP effects might fry any electronics on an unshielded probe.

[Edit] However, this idea is perhaps conceptually less completely barking than his strategy for recovering important hard drives from a defended ship passing through the Panama Canal in The Three-Body Problem. Spoiler ... ... you simply cut the ship (and crew) into tiny pieces using a nano-filament wire ambush, then recover the sliced hard drives from the sea bed and reassemble them. I basically stopped reading at that point.