Motorcycle alternators are a good choice however they aren't always a cheap junkyard item. Only one of six junkyards near me sell used motorcycle alternators and they want a premium for them.
A good source of cheap, used, junkyard alternators are small import cars - kia's, tercel-sized toyota's, nissan sentra's, essentially tiny cars that have a minimalistic set of electric features. The alternators are physically smaller and typically the bearings are far better than domestic stuff for some reason, and they're a dime a dozen pretty much.
Just know that most automotive alternators need to spin above 6000 RPM to produce any kind of consistent amperage and that's done by having a really small pulley on the alternator and a very large pulley on the crankshaft. You'd need to use pulleys that suit your redline of your mower engine.
And just because you selected an alternator capable of say, 65 amps, doesn't mean you're going to get it. In fact, you're not, probably closer to 30 amps as a maximum, though not leaving much horsepower left to drive the kart.
On the plus side, you probably don't need 30 amps to charge a small motorcycle battery and a light or two. A 55W light draws about 4 amps or so.
