Ну вот, исчезла дрожь в руках

At my first amateur look it looks good.

Though there are some things I’d change:
My fear has thrown itself into a chasm
It seems to me too literal. Let’s at least change subject and object:
I threw my fear into a chasm
or better yet
I overcame all my fears (of falling/failing)
Though in the original the subject is fear to give it more drama. Maybe something like this will be better.
My fear let go of me and slipped into abyss.
Среди нехоженных путей
Here undiscovered or unexplored for нехоженных seems better.
are covered by snow
are shrouded in snow
sounds to me better.

And that’s all. ;)