That's a good option. You must determine whether the hard drive is an IDE (also called Parallel ATA) or SATA (serial ATA) drive. Since they have different interfaces and most USB external hard drive enclosures are made for on or the other. The hard drive can normally be removed by removing a screw or two and slideing it out of the case. Be careful to NOT touch the connectors of the circuit board
. You might find that there is a small adapter plug between the drive pins and the laptop. It needs to be removed so that you can plug the drive directly into the new drive enclosure.