Installing Windows 8.1 on a SSD

Just keep it simple, physically disconnect your windows 7 disk, connect the SSD and install windows 8 on that. Once windows 8 is up and running turn off your computer, connect the old disk on another sata port, set bios to boot from Windows 8 disk, and just copy your files off the old disk. You can also boot from the old disk to back up other stuff like your bookmarks, or whatever from within the old system. Keep using the SSD for a couple weeks before you format the other drive to make sure you didn't forget to back something up from your old system, such as browser bookmarks or e-mails if you're using Thunderbird. After that you can format your old drive and use as data storage. There's no need to mess with dual boot in this situation as you don't plan to use both system in the future, from what I understand.

The reason that installing Windows on a new drive with an old Windows drive connected is a bad idea:

The new installation will not have its own boot and recovery partition(s) but rely on the those on the old installation, which means when you unplug your old drive or it dies someday, you won't be able to boot the new drive as well without a hassle.

You'll need to reinstall Windows Boot Manager and rebuild the BCD store with bcdboot, if it's a UEFI installations, you'll even need to shrink your C: to get some space for a new EFI System Partition, and in any case, you'll lost the recovery environment (though some people might consider it useless).

Therefore, in my opinion, it's mostly a better idea to install Windows on a new drive without any old Windows drive connected to the system, so that the new installation will be standalone, unless your motherboard has a UEFI that sucks, for which its boot menu is not accessible or so. And you can always add an entry to the BCD store of the old installation for the new installation (without touching ANYTHING on the new drive).

Put the New SSD and unplug the Old SSD then Restart the computer

Install Windows 8.1 on the New SSD.

When you boot 8.1 up plug the old SSD in.

Move your files from Windows 7 Into 8.1 and Format the Drive when you are done.

After this it will may still show windows 7 in the boot menu with Easy BCD