According to your comment, the narrator paused between the words wine and firm, leading you to read firm as an adjective. This is an understandable assumption, but I think the narrator has led you astray on this.
The expression "You can't go wrong in the hands of X" is commonly used in advertising to indicate the quality of the product or service on offer. Here are a few examples:
... you can't go wrong in the hands of Chefs Alex and Mike
You can't go wrong in the hands of a Master Roaster!
...in need of auto body work then you can't go wrong in the hands of
Kings County auto body shop.
In this case, the governess is saying (in paraphrase):
I recommend XX wine firm. You cannot go wrong in their hands.
Saki has made a relative clause out of the second sentence in the paraphrase. He could equally well have written:
When this one went as far as to recommend a wine firm in the hands of
whom you could not go very far wrong,....
These constructions are formal, but perfectly grammatical.