I don't think that either of these strategies is likely to be appreciated much by reviewers.
Very few papers are actually entirely unobtainable to researchers. Most papers are either part of a university subscription, available as preprint from e.g., the author's website, or at the very least most authors forward you a preprint on personal request via mail. The purpose of a scientific review is to review, to the largest extend possible, everything that is out there.
Limiting yourself to only Open Access material, while morally commendable, means that you are not surveying the state of research, but only the state of what's available easily. This will make your literature review significantly less appealing to reviewers.
Further, I would definitely not go for
Also some papers are accessible from my University without me noticing the paywall so should I rewrite the criterion to "... that are not freely available or included in the authors university contract"?
That just seems like a lazy excuse for not finding out what licence the used papers fall under. Even if the paywall is hidden to you, you can certainly figure out whether the paper would be available without subscription.