Sadly, you can't swap out the HD for a SSD (any vendors) as the system is expecting a thermal sensor within the HD. With that said you can buy from other world computing a special adaptor but no one has tested yet.
Just to be clear, you will be a trial blazer here.
There is just not much info out there on many people even attempting to open these systems as they are very hard to open and making any alterations (different from what it was designed to support).
While I understand your desire to improve your systems speed I don't think swapping out your HD to a SSD is the best solution.
The better direction is going with a hybrid HD (SSHD) than trying to force fit the SSD into the system. That way you won't need the thermal sensor as the drive will have it (unlike the SSD).
We bought a few dual drive'd Thin systems but found the drive just wasn't large enough for what we needed and the system was sluggish as well running a Fusion drive setup in our configuration (CAD and Presentations). We only have a half dozen of these as our direction changed due to the difficulty in servicing this model. We are going forward with the Mac Pro system instead for our new engineering desktops and the staying with the mini for administration desktops.
Seagate makes a nice unit which we have installed in the systems we have. Here's the spec sheet: Desktop SSHD spec sheet. While not quite as fast as a straight SSD it is dam close.