Sawasawa can also mean "equally, correctly, alright", so for example:
"Waligawa pesa sawasawa" they divided the money equally
"Anafanya kazi sawasawa" (S)he is working correctly
"Ni sawasawa kumpiga mwivi" It is alright to beat a thief
As Daktari puts it, sawasawa is almost always used as 'okay'
Eg Pesa si shida, sawasawa? (Money isn't a problem, okay?)
"Kupanga sawasawa" To arrange just right.
"Kupiga sawasawa" To play (an instrument) just right.
"Kupika sawasawa" To cook just right
These are just a few that could think of that I know I use when speaking to my family in Kenya.
Well, in that context - "All right." can also be used in English as "It's ok, we can move on now." But "Let's go on." correctly would be "Tuendelee."
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. :)