Install Ubuntu to a hard drive temporarily external and after that move it to internal?

I am replacing my internal hdd in my laptop with a new one. The new hdd hasn't been used before, and lshw can detect its capacity and no other information.

I think of two ways.

The first way:

• backup the data of my internal hdd to a third external hdd.
• replace the internal hdd with new one,
• install Ubuntu on the new internal hdd,
• copy either the data on the original internal hdd (with a sata-usb adapter) or the backup data on the third external hdd to the new internal hdd

The second way:

• use the sata-usb adapter to connect the new hdd to my laptop.
• then can I format and partition the new hdd and install Ubuntu on the new hdd, while I am running my Ubuntu 12.04 on the old internal hdd (still internal)?
• after installing Ubuntu on the new hdd, I will copy the data from my old internal hdd (still internal) to the new hdd (external)
• turn off my old Ubuntu, and replace the old internal hdd with the new hdd.

My questions are:

1. is it possible to format and partition the new hdd (external to my laptop, and connected to my laptop via sata-usb adapter), and install Ubuntu on the new hdd, while I am running my old Ubuntu on the old internal hdd (still internal)?

2. How good and bad can the second way be?

   For example, do I have less risk of data loss in the second way than in the first way? So I can skip backing up data to a third external hdd in the second way?

Thanks.