"In no way" vs "By no means"

Solution 1:

They are very similar phrases. Both are usually stronger than the raw I am not suggesting.

They both suggest that a reader could attempt to construct a multitude of arguments leading from the preceding discussion to whatever unfortunate suggestion follows, and that every single such line of implicit reason is denied by the author.

That you have added words to this effect suggests that you are defending against such a position and so could be seen as defensive or, in other contexts, merely robust.

A means in this context refers to a process or system designed to some particular end and purpose -- "I will escape the prison by means of a rope ladder"; -- as does a way, by the metaphor of a path from a problem to a solution, -- "I will solve this problem the old-fashioned way". All such means (and ways) of building whatever conclusion follows are denied by the author.

I find it impossible to separate the two expressions.

Some people prefer "I am by no means suggesting that..." and "I am in no way suggesting that" which seem slightly more idiomatic and common than your original construction (a conclusion also supported by search counts).