Different blood lines of Beagles have somewhat different traits. If yours has a strong prey drive, in my experience the only real training you can do is to teach them the basics young.
The big one is "call back" or heal. If you can get a Beagle to quit a trail and come back to you, you have a winner.
Next would be not to run Deer. My Beagles had no quit in them, they'd follow a trail or do hot pursuit forever. I'm talking many miles here. Having a GPS locator on your dog is advisable.
Blood trails, teach then to work off of a long leash. The leash is a pain, but mine made the connection to slow down with a leash. And learned to feel the feedback from me through the leash (somewhat).
Following a hot scent and not getting side tracked comes with experience.
Beagles are IMO hard to train,, it is more a point them in a direction and follow or hold on type thing.
I don't have much confidence most Beagles would be focused enough to hunt sheds. The first hot scent they came across and off they'd go.
My Beagles were hot hunters, had a strong prey drive, weren't much on listening to commands when they had a scent.