Implications of Ares picking her knife instead of reloading her gun before the climax fight

In addition to Kai Qing's interpretation mentioned in a comment, that Ares decided to take another approach to killing Wick that had not yet been proven to be so unsuccessful, there is another reason she might have opted for a knife.

Ares seems to embody an assassin of the silent type: she doesn't, or can't, speak, she follows her prey incessantly and silently, and she uses a silencer on her gun, even at moments where it seems quite pointless (e.g. during the noisy hunt in the 'Reflections of the Soul' exhibition space in the fictional New York museum).
After Wick kills Gianna D'Antonio, and Ares and her henchman attempt to help Santino 'tie up "loose ends"', she is very sparing with her shots in her confrontation with Wick.

It is very likely she prepares a knife in her left hand because she is more proficient with it, and expects to fight Wick in close quarters, awaiting him right behind closed doors he has to pass through to get to Santino.

As for the reason she didn't even prepare for deviating circumstances by reloading her gun, I guess a (personal) code of honour could indeed account for it (but that might depend on the answer(s) given to this question).
There is also a slight chance she has noticed how Wick has taken guns and/or ammunition from some of the guards along the way, and - concluding he is running low on either or both - she wants to decrease the chances of him getting 'more shots' at killing her employer.