Shirk is associating partners with Allah. To my understanding, doing the phairas would be considered as shirk, because Hindu’s say that they are making their vows, “agni ko sakshi maan kay”. The fire is also considered “sacred” and it is a religious element, not a cultural one.
In my opinion, as a believer, she should definitely do her best to please her parents. In other words, for the sake of her parents, who no doubt must be going through hell with the idea of their child marrying outside her faith as it is, she can incorporate the non-shirk elements that they really want to have but should exclude the shirk-y ones, in accordance with her new faith.
Btw, for whoever was saying their vows would not be valid-- since the girl is converting to the guys faith, their vows would definitely be valid…