If you don't want OS X on your SSD and only Windows, then you will need to do three things.
1. Create a boot-able Windows USB using Boot Camp Assistant and a Windows ISO, this should also have the necessary Boot Camp drivers which you can check for at the root of the USB drive (Look for a 'Bootcamp' folder as well as something like WINPE-DRIVERS). If you want, make sure it boots as it will be hard to make another one after the next step.
2. Boot into Internet Recovery by holding down Option+Command+R and staring the computer, you will need to connect to a network over Wi-Fi (or Ethernet using an adapter). Once in Recovery open Disk Utility and erase the entire drive using the GUID Partition Table and MS-DOS (Fat32) as the file system.
3. Use the boot-able Windows USB you made to install Windows by inserting the USB, holding Option when the computer starts then selecting 'EFI Boot' (don't select 'Windows' or it will complain that the hard drive cannot be partitioned as 'GPT' once you get to the hard drive selection). When Windows install asks you to select the drive to install Windows onto, select the largest drive and select 'Drive Options (Advanced)' -> 'Format' then install Windows like normal. If all goes well you will have a MacBook Air with Windows as it's sole operating system.
As for your Windows 8.1 activation key, I am not sure that it will still work to activate Windows 10 even though you have upgraded in the past but might be worth the try.