Yes I have an external hard drive as well, but it doesn't have its own power source so i'm a bit concerned a laptop won't power it
Go for it. My laptop is quite iffy on power from it's USB ports (lots of warnings in the early days with USB thingees) but I've never had an issue with recent external drives, up to 1tb. Take you lappy into the shop; they could try a an external drive in it for you.