You wouldn't dare touching any radioactive element? So, you wouldn't eat, say, a banana? You are radioactive, as is pretty much everything you eat, and the ground where you live, and the air you breathe. Radioactivity is everywhere.
Most of the radioactivity in humans is from potassium-40, and a bit from radioactive carbon. Potassium-40 is more radioactive than U-238.
Of course, this is mostly a jab at your "I wouldn't touch anything radioactive". The popular understanding of radioactivity is dangerously bad, which is why people are afraid of nuclear fuel more than, say, the waste out of a coal power plant or of their own wood-burning furnace.
The main risks you have when handling something like a pellet of U-238 is:
- It can be ingested. Uranium is one of the more dangerous here, because it easily produces shavings that can move in the air and burn quite easily. U-238 decay mostly emits alpha radiation which is relatively harmless to humans, as long as you keep it outside. Needless to say, it becomes a lot more of a problem when it sticks to your lungs and gets into your blood (though that already poses extra problems due to it being a heavy metal - it's highly toxic regardless of its radioactivity).
- It's very concentrated - you're holding a big slab of radioactive material. The potassium in a banana is highly radioactive, but there's so little of it that it doesn't pose a real hazard.
As long as you keep your gloves on and isolate the air (as in the video), you'll be fine, especially if it's something you dug from the ground - danger from radioactive source is inversely proportional to lifetime of that source; uranium must necessarily have very little radioactivity, since it's existed as long as the Earth and there's still plenty to go around.
Don't mess around with those radiotherapy sources, though (warning: very much not pretty with a lot of "how could they be so stupid"). If you decide to read about that incident, note that even with the vastly more dangerous radioactivity source, the serious health issues (including amputation and death, sadly) were a result of a long exposure (many hours) and/or ingestion.
Needless to say, this shouldn't be taken as an advice to go ahead and play around with highly radioactive stuff. It is dangerous, just like, say, mercury is dangerous. It can kill you. All facilities dealing with highly radioactive matter have strict measures to prevent accident and measure exposure, and the gloves you see in the video aren't your typical household cleaning gloves. Different radioactive materials can have vastly different dangers, depending on their half-time and the emission characteristics.