I would use a pre-qualification company, like Site Wise or Impac Prequal. They're relatively inexpensive and will take a look at your systems in place and identify any gaps you might have.

Might be a silly question, but have they looked at the SafePlus free self-auditing tool?

Simple to use, uses plain language and developed by the regulators ... :)
https://online.safeplus.nz/

Just because you don't need to hold certification doesn't mean that these standards aren't useful auditing/management tools.
An external auditor can still audit to one of those standards, but if you have the discussion with them about what you want prior to the audit, they should be able to tailor it to your needs. There may well be parts of them that aren't applicable and you can safely put aside.

Yes we've done that. It was fine but we found some limitations with it. The next step would be to have an assessor come in, however I am searching to see if there are other options before committing to it.

Outside of using a registered safety professional from the HASANZ register to conduct an annual audit against legislative and good practice standards, they could consider the TELARC product 'Q-Safe' certification. From experience this is a well put together standard and I believe is backed by WorkSafe, CHASNZ and the EMA. Not half as expensive as an ISO certification and worth a look.

For an SME who does not hold, nor needs to hold, any certification to standards (4801, 45001 etc) I'd just pull out the old NZ4801, the ACC Self Assessment resource. Keep it simple. It is weighted towards documentation rather than behavior but with a bit of sense its not hard to mix the two.

We are entering austere times. A bit of frugality mixed with practicality can go a long way.

Hi Amy
Find someone who knows what they're talking about and invite them in for a fact finding discussion and then a review of effectiveness. Once they know what you do and what you intend, they can select a framework to do it. Any worthwhile auditor will be able to draw on a range of sources plus their own experience to give you an indication of what you're doing well and where you could juice things up a bit. In my previous role I developed this process https://www.advisian.com/en/what-we-do/services/asset-advisory/strategic-asset-management although here it has been co-opted by the asset management team. The first two steps mean that the actual review is targeted on what you need rather than wasted spending time reviewing a list that some committee thought up without any context.