Looks right. I found a stainless plug with a large Hex/Allen head. It fit well, but was raised above the deck—a hazard.
But it is now I find the same "fix" is a set screw—and doesn't need filing. They're available at Home Depot and Amazon.
It does require that Hex/Allen wrench (above) to install and remove. (Although grinding the top with a straight cut would assist routine removals using a standard screwdriver or a coin).
Whatever is installed, it should be wrapped with a turn or two of Teflon tape to ensure it won't get stuck.
I tried to buy one from Sunfish Direct, dating my boat carefully from its serial number. SD sent me the wrong plug, and their customer service ignored me, so I'd be wary of relying on them to sell you a replacement. As others have noted, corks work, although can get kicked loose when coming about.
It might be better all the way around to get the entire old plug and threaded insert out, and install a nice new plastic one that comes on new Sunfish. It doesn't seize up, is easy to open to drain the boat if needed, and if you lose the plug more are available.
I use one of these, like I do on my transom drain. Tie it with a piece of string so you don't loose it if you flip and it is unplugged. The old Despersia drain unplugged, drains faster than either the new plastic ones or the old Despersia with the cap lightly screwed on. Easy to quick plug in and pull out too. I've never had an issue.