Quick links or master links are easier. Especially if you are going to be taking it off to clean regularly. They do need to at least match the speed that the chain was made for. I'm even pickier on that and will want to match the brand too.

However you can just push the pin back in. Many might gasp in horror at that though. But I did it with a 11 speed chain when it was new and it never gave any issues during it's entire life. In my case I would have gone out to get a quick link or the break-away pins Shimano was using with their chains at that time. But it was late on a Saturday night. And I wanted to ride the bike the next day.

The fact your pins protrude from the side plates makes me doubt that is a proper chain for a 10 speed. But possibly it's the picture enhancing their look.

Or are you multiplying the sprockets on the rear by the sprockets on the front. We don't do that today. That went out of style a decade before the turn of the century.