I would not call in sick.

What if your current company tracks your JS to MEM?

Now you get fired for lying. Not good.

I would call FedEx, explain the situation, explain that you bid around it, but you have zero control over your training. Be honest with FedEx, and ask for another interview date. If they are smart (and I hope the hiring people are, but sometimes I wonder) they will let you reschedule.

Don't lie to your current employer and get fired over it, that will ruin your long term chances anywhere else.

Be honest, it's the right thing to do, and I think the smart play as well.