For me there is not much difference between "It's OK we can move on now" and "Let's go on" It has a similar intention to me. I do not care very much about literal translations. The fun part of language is that there is something to choose and there is so much more than formal language. So I would be very careful saying a translation or wording is not correct.
What I meant to say, is that "Let's go on." is a narrow translation based on your situation. In other situations other translations would work better - for that I added background/more information.
And I study these things at university - technically there are wrong translations. (Like saying "hi" is a greeting also used when saying goodbye or translating an animal name as another animal it does not refer to.)
And "Sawasawa." does NOT mean "It's ok, we can move on now." That is the stretch of "All right." (so can be used that way in that specific situation). In other situations "All right." would be interpreted differently - that was the point I tried to get across; sorry for not being more specific. :)