Why a belt drive??? Why not just stick with chain?
Because the kart already has a cog belt sprocket on the axle?
Guess it depends on what the OP has in mind for the future... Chain sprockets are much easier and cheaper to switch around drive ratios since they're more common and readily available. If you want to go faster, you slap on a different sprocket and add/subtract a few links.
Cog belt sprockets are way more expensive and harder to find.
For right now, the quickest and probably cheapest way to get the kart going is to buy the cog belt clutch, but for future upgrades, chain and sprockets will be more versatile.
HOWEVER
that kart is clearly NOT set up for an industrial engine. It will require modification to make one fit. Odds are, the shaft won't be in the exact right spot to make the belt line up, which means you'll probably have to move the sprocket one way or the other on the shaft and possibly install a different length belt, which will mean pulling the axle off. If that's the case, you'll already be doing most of the work needed to switch to a chain drive.
I don't see any obvious reasons why the hubs and sprocket and bearings shouldn't come off. It's not excessively rusty. A little fine sandpaper on the surface rust on the shaft, and some penetrating oil, and it should be quick work.