  Starting from the QCD Schroedinger functional (SF), we define a family of
renormalization schemes for two four-quark operators, which are, in the chiral
limit, protected against mixing with other operators. With the appropriate
flavour assignments these operators can be interpreted as part of either the
$\Delta F=1$ or $\Delta F=2$ effective weak Hamiltonians. In view of lattice
QCD with Wilson-type quarks, we focus on the parity odd components of the
operators, since these are multiplicatively renormalized both on the lattice
and in continuum schemes. We consider 9 different SF schemes and relate them to
commonly used continuum schemes at one-loop order of perturbation theory. In
this way the two-loop anomalous dimensions in the SF schemes can be inferred.
As a by-product of our calculation we also obtain the one-loop cutoff effects
in the step-scaling functions of the respective renormalization constants, for
both O(a) improved and unimproved Wilson quarks. Our results will be needed in
a separate study of the non-perturbative scale evolution of these operators.
