I would probably move forward based on the following two assessments:

A) by a site's traffic figures, content quality, and backlink profile (assessing this within reason). If they receive a lot of traffic, produce great content, and seem to have an appreciable amount of good quality links, then the site in question is very likely "good" and "trustworthy"

B) by the the types of links that are being provided to the site in question. If a certain instance of a link is not promotional, unlike in the case of a sponsored review, then this criterion checks out

If both check out, then I would say it's safe to remove the "nofollow" tag for that particular link.

Now, thinking about things holistically, I would say that if the site does not link out to a degree that seems above-average or high, then I wouldn't worry about potentially "following" nearly all of your links again. You received the penalty because of the the nature of the linking, the specific links that you linked out to, and/or the volume of external linking.