The section 9 of the Defence Act provides the Minister of Defence with the authority to use the NZDF for public services and civil purpose but requires notification to the House. The Minister's authority lasts 14 days whereupon it lapses unless extended by the House (or in its absence, the GG).
There is no similar requirement of notification of authority by the House for overseas deployments where force is expected to be used.
Even though it seems like a core Executive Prerogative, I think the Minister of Defence could be required to go to the House and ask for its authority to use the NZDF overseas and to use force. This authority need only be given once for a particular overseas action. However, once the deployment was finished any subsequent action in the same place would require a fresh authority. If the Minister gets the authority of the House, s/he can subsequently authorise further deployment of troops for the action authorised by the House. This avoids the need for the Minister to keep going back to the House asking for authority to send another group of troops to the action.
Given New Zealand's forces are for defensive purposes, I don't think it's an unreasonable assault on Executive power to have the House (or in its absence, the GG) specifically authorise the use of troops for military action. It's not only democratically sensible it's also a practical consideration given the House is going to end up having to find the resources to continue the engagement.
While this is deeply controversial and mired in heavy constitutional principles about Executive versus Parliament's powers, I think it's a worthy cause. Keith Locke would be the obvious candidate to promote this.