Titebond 3 is an aliphatic resin glue and it is available in New Zealand. I have not used it, but I got this useful email from Dave Z (triloboats: Wayward) and I am sure he won't mind me posting it here. I believe it is a very good glue, but Dave has used it for a deck covering in conjunction with acrylic cloth reinforcement, as a way of avoiding the use of epoxy.
"Our TBIII / Acrylic decks are now in their third year, and are looking great. I'm starting to hear of more successful probes from the internets. So the method seems solid.
Our TBIII source was Home Depot. Ordering online in 2x1gallon packages (postal delivery) came to about US$26/g plus shipping. Deliveries to any of their stores for pick-up was free shipping.
That's going to be a little more difficult in NZ... maybe via Amazon? Amazon Prime shipping is 'free' (after monthly membership), and Alaskans rely heavily on it. Maybe they have some arrangement to you?
Our 2oz (?) woven acrylic was purchased from Jamestown Distributers (they have an online store), for about US$22/yard x 56in. It was called Dynel although that is no longer in production. Personally, I think any lightweight woven or knit acrylic would be optimal (acrylic is very wear resistant and is used over fiberglass - in kayaks for example - to protect it from abrasion). I wouldn't hesitate to use any synthetic cloth.
The method is a descendant of using a latex lagging compound to saturate just about any cloth. Burlap was popular (!) since it was so cheap, but I lean to synthetic (on the advice that if water does penetrate, it's immune to rot). Lagging is the fabric wrapped around hot water pipes to insulate and protect people from contact burns. The compound is cheap and waterproof when dry, and sets up to a relatively soft, but easily repairable deck.
This may be a more available choice for you. Better yet, it's cheap and easily removed/replaced (just peels off). Burlap was good for about 15 years, I've heard. Our LUNA's deck (lagging compound on fiberglass cloth) looked very good at 21 years (I'd go for cloth, rather than fiberglass, these days, as cheaper, easier to handle, more pleasant to work with). "
While on the subject of deck coverings here are another two possible alternatives to epoxy, for consideration:
1. Thickened acrylic resin with glass chop strand mat. I did that on a domestic deck 20 years ago, with just a coat of alkyd undercoat as a prep, on cheap plywood. It was a proprietary product (Deck Tread), not cheap but very user-friendly (wash hands and rollers with water etc). It is slightly flexible and wrinkled at the unglued plywood butt joins (rather than cracking). Never heard of it being used on a boat, but I can't see why not. The membrane is still intact and as good as new after 20 years under our harsh sun, having had just one re-coat of acrylic about 5 years ago. Non-skid surface. Possibly not able to withstand rupturing (hobnail boots etc) or too much abrasion. MUCH easier than using epoxy. The idea is food for thought anyway.
2. I'm currently trying a few things with water-borne epoxy resin which I have used in a number of ways over the years, including thickening with portland cement and fine sand. Had very good results over 50 years as a surfacing for cementitious surfaces in marine applications. Again, hands and tools can be washed with water - sort of - and it doesn't have the heavy solvent smell of conventional epoxy so possibly might be more user-friendly for someone who has become epoxified. Possibly not suitable for structural purposes but proven as a surface coat (water-borne epoxy resin is the basis of coppercote antifouling). I'm fooling around with it again on a current project. Just bouncing ideas here. I think it would be easy to use with either glass or acrylic reinforcing and will be trialing some ideas this coming summer.
3. I shredded a sheet of plywood once, tryinh with great difficulty to remove a recently-bedded-down cockpit floor fastened down on a polyurethane rubber sealant (which I had mistaken for silicone rubber). In some particular applications polyurethane rubber would be a better glue than epoxy, but perhaps not for the work you are doing at present. There will be others who can advise better on this class of glue - and other alternatives I am sure.
Prior to epoxy resins we used wood preservatives such as copper napthate ("metalex") and for glues we used urea formaldehyde glue, and resorcinal glue (with the lovely smell). In my view epoxy is the best, but not the only solution - and not worth it if it is poisoning you.