This is on the output of the 7805, right? The cap is the reservoir the driver will lunch off of until the 7805 can refill it.
A 470uF 6.3v cap is about 12mm tall and 7mm dia. That's not that big.
But if it is, you can spend a few more pennies and buy a tantalum cap. Much smaller, about the size of an M&M (without the peanut).
If that's still a problem, use a smaller value cap if you have to.
Good catch. "If" isn't the operative word. I'm certain that any problems will not be on the hardware end, provided I don't cross my wires. Scoping the outputs should be pretty exciting too.