I don't think you need to worry so much about damaging the data as much as damaging the enclosure. The drive should be a standard 2.5" or 3.5" drive. Locate all the screws on the enclosure, remove enough of them to gain access, then disconnect the power and data cables from the drive.
Some enclosures are easy to open and put back together. I've run into a few that have rubber molding around the edges and sometimes the screws are hidden under the molding. Getting the molding off is easy, putting it back on later may prove to be more difficult. It will run fine without the molding, it just won't look as pretty.