The term "unguiltily" can be a bit tricky to find synonyms for, as it is a somewhat specific word with a limited range of meanings. However, a few options might be "innocently", "blamelessly", "unimpeachably", or "unconsciously". Each of these words conveys a slightly different nuance, but all convey a sense of doing something without feeling guilty or responsible for any negative outcomes. Whether you are trying to describe someone who is acting in good faith despite potential risks, or simply trying to find a way to talk about a situation where there is no clear culprit, these synonyms for "unguiltily" can be useful tools in your writing or conversation.