Clone older hard drive over USB 2

I am trying to upgrade the hard drive in an old work laptop (Acer Aspire ruing Windows 10), but I'm having trouble getting the data onto the new drive (7200 rpm SATA 6).

I'm following this article about how to clone a hard drive then boot from it. Seems simple enough, but the issue is that you need a way to have both hard drives plugged in at the same time so you can clone the data from one to the other. They recommend using a SATA/USB adapter, but I'm not sure that the new hard drive I purchased will be adequately powered by a USB 2.0 coection. The box says it requires 5V and 800ma. My understanding is that USB 2.0 can only provide 500ma.

I don't know much about electrical engineering so I'm not sure if I'm correct. Assuming I am, what other options do I have? I just need to move the data from one drive to the other.