It's a possessive adjective, not a genitive pronoun. The genitive would be "Kesy yno korze issa?" which would be roughly equivalent to "Is this one the sword of me?" Grammatical, maybe even understandable, but not something a native speaker would actually say.
For more on this, see http://wiki.dothraki.org/High_Valyrian_Pronouns.
"Bisy" is for animate nouns, so (as I understand it) people and animals. So I guess you would only use "Bisy ñuha korze issa" under very peculiar circumstances... for example:
If you were trying to imply your sword was alive (Stormbringer??)
You were calling a person, metaphorically, a "sword" (perhaps you are a Westerosi lord talking about one of your "Sworn Swords"?)
And that's weird enough as it is, but the circumstances would be even stranger if you were asking this as a question.
Ah I see what you mean now. Thanks for your help. I have another question though - is birds/bird an animate noun or inanimate because I've been having to use the inanimate k class for it? I guess it would make sense, for example if bird was just a classifier e.g. that bird is an owl. I'm not sure though. I hope that made sense.