I agree with A&B and would not do the leash at all!!!
Besides the fact that they can slip out of them easier than you could imagine (ask me how I know) they also can hurt themselves very badly if they get scared and try to run – they reach the end of the harness/leash length and it snaps them back.
This can cause them to break a leg or worse – their back paralyzing them.
Just like some treats – just because they sell it in a pet store doesn’t mean its safe – I promptly through mine out.
What I do for mine to take them outside is I bought a pen – I carry them outside in a pet carrier – I then get in the pen, secure it behind me – let them out and then sit down in there with them. ** You need to stay in there with them because my friend put hers out, went inside for a few minutes, came back out and a stray cat had tried to get it through the bars (she had covered the top) but the bunny freaked out so bad trying to get away and out the other side it actually broke its leg.
Also, be careful if you take them to a public park as they can use pesticides on the grass which could harm your bunny when they groom themselves.
Taking him outside is still a GREAT idea! You just need to do a bit of research and buy/make the appropriate pen to make it workable.