I don't know about a sling shot. Since Sea lions rarely expose more than their head, what are we shooting at? A target the size of a soccer ball from 20 yards on a rocking kayak. Good luck with that. I'm pretty good with a wrist rocket, and have killed both squirrels and rabbits with them. That's going to be a tough shot to make. And lets say you bulls eye your target. Pretty good chance of seriously injuring the sea lion. If you had to get them off your dock, and could aim for a body shot, I would be on board.
regarding the pellet gun, with a blunt tipped pellet and a gun shooting less than 500 ft per second, you would be safe knowing it would not penetrate the skull. And that gun would fit the bill. The semi auto is nice, but way less accurate, than a Crossman 2250. Available at Walmart for $60 or so. And there are a ton of after market upgrades, if you want. Only one shot at a time, but ding in the back of the head once and he'll take off. or get mad and flip you over
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However, just know that pellet guns are not non-lethal. I read an article thru a link on an airgun forum a while back. A man was arrested and fined for killing a deer with his air rifle. He was just trying to scare the deer away from his garden and shot the deer in the body with a .177 Crossman. The pellet traveling around 900 fps, pierced the skin and slipped between 2 ribs puncturing a lung. The deer died a few days later. Fish and game did an autopsy and some investigating. He was charged with Discharging a firearm within city limits, and hunting deer out of season. Aside from the fine they revoked his rights to obtain a hunting or fishing license for a few years. On the other hand you could pick up a . 40 cal Pre charged pneumatic air gun and we could go hunting sealions. I wonder if they taste good.