Often, the universe is considered to be everything by definition. Physicists would use this kind of definition but make it weaker by speaking of the observable universe, i.e. the part who's existence we are sure about.
A) Universe: Everything there is
B) Observable universe: Everything that can be known about (right now)
If the first case, there is nothing that exists outside the universe and there would be nothing you could do about it. You could never get "outside" of it, because it always contains you, no matter where you are in (or not in, for that matter) space-time.
It sounds more like you are talking about the observable universe, which may or may not have nothing outside of it. It's not generally considered practical to get outside of the observable universe, and scientist often use "universe" instead of "observable universe" because they are trained to avoid speculating on things that are thought to be unknowable.
This is important, because there are now two meanings of nothing, so that when I say "there is nothing beyond the universe" it can mean
1) There is no X such that X is outside the universe (from A)
2) There could be something outside the universe, but it is inconsequential (from B)
This makes the language quite tricky, generally "nothing that is P" refers "there is no X such that X is P", nothing is not a thing. Yet, if we are talking about the observable universe, the nothingness outside the universe might actually refer to something. Leading to a very strange usage of the word 'nothing' as "things which we don't know about". This is a source of confusion.
If there is actual nothingness (1) then you are asking about the impossible. If there is "epistemological nothingness" (2) then the best we can say is "who knows!" (though the cosmological principle would suggest that it would be very much the same as here)
Would you cease to exist or could you actually exist in nothingness?
In actual nothingness (1), you would cease to exist (though its better to say that you can't go there), in "epistemological nothingness" (2) you can go there, but we can only guess as to what it is like.
But if you assume that there is nothing beyond our universe
Then you are restricting the answer to actual nothingness (1).