Why West Germany would not have received Prinz Eugen

Could Prinz Eugen have been retained and commissioned into the West German navy in 1955 instead of being used in a nuclear test?

No. The powers controlling postwar German rearmament would not have allowed West Germany to keep the cruiser.

The counterfactual keeps Prinz Eugen out of the nuclear tests and asks whether the cruiser could join the West German navy in 1955. The occupying and allied powers would not have permitted the transfer. The decisive barrier is therefore the politics of rearmament and postwar control rather than a technical question about recommissioning the hull. Alliance permission and the international status of a defeated state could determine naval procurement.