Interestingly he said that he might go for more than one sport. Let's go crazy and take a look in which all sports he could possibly compete if he aims to take part in as many as possible.
Universality sports
Athletics - almost any individual event if selected by Tongan NOC
Swimming - any individual event if selected by Tongan NOC
Easily achievable continental qualification
Judo - Just participating at couple of qualification events should be enough for an Oceanian continental place.
Sailing - Just participating at a qualification regatta likely enough for Finn, RS:X, 470, 49er and Nacra. Might face a couple of nations in Laser.
Taekwondo - Already qualified there for Rio. Should be easy enough if Australia doesn't choose that weight.
Possible continental qualification
Archery - Could become possible if Australia gets a quota before the continental qualification, however island nations are not that bad here (including Tonga).
Badminton - If Australia again decides to decline men's singles quota, then he could get a continental place. Quite possible, Tonga itself almost qualified for Rio but it turned out that their player didn't have enough international tournaments to be eligible.
Canoeing - Both slalom and sprint are possible, though Oceania does have decent athletes outside of AUS/NZL... I guess C1 (200m or 1000m) in sprint might be the best chance.
Artistic gymnastics - Should be able to qualify through continental qualification event, provided that both AUS/NZL qualify before.
Open water swimming - Could qualify if both AUS/NZL qualify directly and/or decline.
Tripartite commission invitation
Boxing, Trampoline, Modern pentathlon, Rowing, Table tennis, Weightlifting, Wrestling (+ Archery, Badminton, Canoeing, Artistic gymnastics, Judo, Sailing, Taekwondo)
So it's possible for him to compete in 16 sports. However, he may struggle to reach minimum eligibility in a couple of them (I already excluded shooting for example because reaching MQS there is probably impossible). Also, I don't think Tripartite Commission would be that lenient for this cause.
Anyone wants to suggest this to him and make a complete mockery of the Olympics? @heywoodu perhaps?