These days, there are plenty of completely free disk partition software programs that even the novice tinkerer will love. Whether you're expanding your Windows system partition, shrinking it to make room for an operating system dual- boot setup, or combining your two media partitions for those new UHD movie rips, these free disk partition tools.
Forget the clueless 'Microsoft Support Engineer'.
Your idea is excellent. With respect to Windows 10 activation: changing the hard disk does not affect activation. You will need a license for Windows 10 only if you change the motherboard and/or CPU.
Cloning your HDD to the SSD is the fastest and most reliable way to migrate. However, I would choose an image rather than a clone. The difference between a disk image and a disk clone is that the former omits empty sectors. This will be important if, as is usually the case, your SSD is smaller then your HDD. Imaging software is also more flexible and so easier to work with. Cloning is better if you're doing a forensic examination of a drive. In that case you want to keep everything. Cloning is also the way to proceed if, like some, you have a sled in your computer so you can easily swap drives. This is great for software testers.
The procedure for moving an image is pretty straightforward but there are some fine details to be mindful of. For example, you want to avoid having two bootable partitions in the same computer, although this is not usually a problem. And you don't want to have two drives with the same drive letter. Do some research on the web and you'll be fine.
Enjoy the speed!