You either have read or read and write access to shares on the NAS. If you have write access, this means you can also delete, overwrite and rename. Unfortunately, to be able to "write" the recordings, you will need to have "write" access to the share. Whether or not it would be possible to configure your software to login to the share, yet not have the logged in user able to access the share with write permissions, I don't know.
Depending on the number of users on your setup, I would also question the performance of streaming audio from multiple destinations to the NAS. This particular NAS isn't very fast.