I wouldn’t recommend a harness, especially since he doesn’t like being handled. The risks of injury are very high if he spooks while wearing it. In general harnesses require a lot of training to be used. As cute as it is, it is really dangerous to have a rabbit on a lead, especially out in public. Plus, many rabbits hate it! As territorial animals, most rabbits are happiest in their home turf and can get very stressed and scared when in unfamiliar places (especially ones with dogs, hawks, cars, etc).
It would be much safer to set up a penned area outside, and train him to go into his carrier. A lot of members have successfully been able to train their buns to go into carriers, so you could use that to go in and out.
One thing to look for is whether any rescues in your areas have “hoppy hours”. I used to take my buns to hoppy hour and 1 of them loved it, the other three hated it and would just sulk in the corner until it was time to go home.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.