If I understand correctly, you are looking for a way to phrase the sentence that will follow the one you gave under context.
There are two issues that should be addressed with these phrases:
- The phrase 'same issue' - are you talking about the issue your answer refers to, the issue that you are currently dealing with in your answer? If yes, I would use the phrase the issue at hand
at hand (formal)
c) needing to be dealt with now: Peter turned his attention to the task at hand. (LDOCE)
The potential mix up of various uses of the nouns way and path
- they can be used as synonyms meaning:
a road, path, direction etc that you take in order to get to a particular place (LDOCE)
which is not the meaning you are looking for;
- 'way' can be used meaning:
a method that you use to do or achieve something:
In this sense it is used: The way to solve/resolve the issue. As in: There can be 2 ways to resolve the issue of energy shortage: finding an alternative source or reducing consumption.
You do not follow a way (this is the problem with your option #2). A way that you follow is usually a physical one (just follow the way until you reach the next crossroad, than turn left). (!There are exceptions to this, but they don't apply here.)
If there are several ways to do something, you can choose one. Although at first your option #1 sounded a bit ambiguous (the way we chose - is it referring to the way that you chose or the choosing strategy you applied?), in this context it is clear what you mean, so this option is fine.
A course of action or way of achieving a specified result
The course or direction in which a person or thing is moving (ODO)
This is often used to describe someones career path for example.It is more idiomatic to say that you follow a path than a way in this sense. Again, if there are several possible paths, you choose one of those.
You might say something like:
The answer to this question will depend on the choice of the path that we would follow to resolve the issue at hand.
While this is a grammatically correct sentence, and there are examples of usage to follow a path in various texts (in social science, physics, law etc.) I am not sure this is the best (most natural sounding) way to put it. That is, it may not be a bad sentence, but it may not be a perfect one either.
Having considered all this...
Essentially it seams that your examples convey the same meaning as the sentence you provided in the part you marked as context:
The answer to this question = the approaches we will offer
the way we view the situation => the choice of the way/path to solve this problem
way/path = approach
So, unless there is a need to say this twice, the sentence: Depending on the way we view the situation, we will offer radically different approaches to this problem. is by far the best one.
Best Answer
They cannot choose to live in a fairy-tale castle because no such castles exist. So we cannot say 'they chose'. But if such castles existed, they would choose to live in one.