Let $A$, $B$, and $C$ be 2-categories (or bicategories, etc), and let $F,F':A\to B$ and $G,G':B\to C$ be 2-functors (or pseudofunctors, etc). Now let $\alpha:F\Rightarrow F'$ and $\beta:G\Rightarrow G'$ be pseudonatural transformations, where the naturality square only commutes up to (coherent, natural) isomorphism.
How can we define the horizontal composition $\beta\,\alpha:G\circ F \Rightarrow G'\circ F'$?
There seem to be two valid choices, namely, the pseudonatural transformation of components (for each object $X$ of $A$) $G'(\alpha_X)\circ \beta_{FX}: GFX\to G'F'X$, and the one of components $\beta_{F'X}\circ G(\alpha_X)$. Since $\beta$ is only pseudonatural, these two choices are technically different (albeit naturally isomorphic).
Is there a canonical one, to use in definitions, theorem statements, et cetera?