For certain matters the henselization $R$ of $\mathbb{Q}[t]$ at $0$ is a 'reasonable approximation' for $\mathbb{Q}[[t]]$ (Artin's approximation theorem and so on). Now, I would like to study certain ('etale) cohomological properties of a finite type $\mathbb{Q}[[t]]$-scheme $S$; I would like to say that there exists an $R$-scheme $S'$ that is 'very similar to $S$' ('from the cohomological point of view'). What are the possible methods for doing so? I guess that I should embedd $S$ into a 'family' and then apply either Artin's approximation, or smooth base change, or both. Yet I would certainly be deeply grateful for any hints (and references); in particular, where can I find an argument for presenting $S$ as a 'member of a family'?

I can certainly say more on these cohomological issues; yet they are rather specific.