Some celebrants will want both of you present for the NOIM. Just find one that doesn't require both of you present.
I would think not having a NOIM or letter from a celebrant would be a bit risky. One of the requirements if that you will marry within 9 months. If you do not have a letter or NOIM at time of lodgement then you are not fulfilling the requirement.
Agents on this board have commented recently that the evidence for intention to marry is at time of application. If you have a letter from a celebrant then yes, you could lodge it but having neither I would not risk it.