Sorry for such a late reply to the page, but TJ nailed it. Arm pump is a result of too much blood rushing to the forearm muscles. While it’s important for them to be strong enough to handle steering loads and vibration, making them bigger will also cause them to require more blood, increasing arm pump. Sounds backwards, doesn’t it? Forearm muscles are best conditioned by driving the kart. Looks like everyone else so far has provided pretty solid advice, so I won’t regurgitate it all, but get some practice and figure out what’s really causing the problem, and make sure you’re not holding the wheel too tight.
If you feel like you need to grip the wheel super tight so your hands don’t slip, try some tennis racket tape. It makes the grip bigger, softer, and stickier, all good things for easing the load on the forearms and hands.