What The_Prophecy said is one way of doing things; upgrade now and just do a clean install or drive clone when you get your SSD.
If you don't want to upgrade now, I believe the latest Windows 10 builds allow you to activate with a valid Windows 7 or 8 key. So you could download the Windows 10 media from MS and just do a clean install when you SSD arrives using your Windows 7 key.
Either way, if you plan on clean installing Windows 10 on your SSD, you are going to want to disconnect your old drive from your PC before you do so. The Windows installer is known for being kind of stupid when it comes to picking a boot partition when more than one drive is installed in a PC, especially if one drive has an older version of Windows on it. So when you install windows 10 you are going to just want to have your SSD connected. You can plug your old HDD back in when you are done.
As for uninstalling Windows 7 on your old drive, that can't really be done. The best you can probably do is try to delete the Windows and Program Files folder along with any folders you no longer need, though you might run into some permission errors on Windows (not sure, I don't think I've never done this). Your other option is to temporarily copy over any data you want to keep to your new drive or to an external drive, format the old drive, and then copy the data back onto it.