  We introduce the notion of Drinfeld twists for both set-theoretical YBE
solutions and skew braces. We give examples of such twists and show that all
twists between skew braces come from families of isomorphisms between their
additive groups. We then describe the relation between these definitions and
co-twists on FRT-type Hopf algebras in the category $\mathrm{SupLat}$, and
prove that any co-twist on a co-quasitriangular Hopf algebra in
$\mathrm{SupLat}$ induces a Drinfeld twist on its remnant skew brace. We go on
to classify co-twists on bicrossproduct Hopf algebras coming from groups with
unique factorisation, and the twists which they induce on skew braces.
