This answer may be longer than you expected, but there's a bit to unpack here.
The translation actually goes the other way. "Facilis descensus Averno" is from line 126 of book 6 of the Aeneid. Either Latin phrase would be an OK (but not ideal) translation back of the English, but "Averno" would be slightly unusual for "path to hell" absent the context of ...
"Per aspera ad abyssum et per abyssos ad caelum"
Is this correct or will I make a fool out of myself?
Yes, that's correct. You might also like
Per aspera ad abyssum, ad astra per abyssum.
Since your sentence is Dante's journey, I leave this grand verse here:
"E quindi uscimmo a riveder le stelle" (Inferno XXXIV, 139)
“and thence we came forth ...
As Latin lacks articles, when translating into English, one supplies them (or not) as appropriate to the meaning. The cultural context only matters if it casts light on the meaning. Assuming it is clear without cultual context (but just by reading Seneca) that Seneca did not mean that each person is helped to be good by a god who may be different from ...