Sure, that works.
Is it correct to translate that into “Wir gaben uns die Hand und gingen unserer Wege”
Sure, that works.
Sounds like the ending of a typical German date. Did you enjoy the walk?
Ich fände besser: „Wir gaben einander die Hand ...” Je nach Kontext dann deine Version oder „ ... und gingen getrennte Wege” oder „ ... und jeder ging weiter seinen Weg”.
it sounds a mess
Using reflexive pronouns like "uns" to mean "each other" is very common in practice, but offends many people's sense of linguistic logic; "einander" is certainly better style. The case after "gingen" surprised me a bit; your version does exist in very formal language because "seiner Wege gehen" exists, but in more ordinary language this would be an accusative, "gingen unsere Wege".
in more ordinary language this would be an accusative, "gingen unsere Wege".
No, that sounds very unnatural to me. "Gehen" is rarely used transitively. "Ich gehe meinen Weg" works for saying that I do my own thing, but not for saying that I walk away from some situation. On the other hand, "wir gingen unserer Wege" is a common fixed phrase.
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