First like to dispel something, you won't get 'SSD' speed out of a SSHD. SSHD takes a low slow 5400RPM (what your 6 yr old HDD sounds like it is) and places SSD Chips as a 'cache' in front of it. OVER TIME (like months) it will 'learn' what to cache ahead of other things, and thus 'load faster', as in on par with the same priced 7200RPM drive you could have bought instead.
If you want 'Fast' Windows loads, and increase performance (i.e. get Windows out of the way with it slow 'how do I make this font on the wall in the game' responses) you can only succeed by going with a SSD drive as the OS drive only then the 2nd drive as the Game / Data drive.
You have to 'rebuild' everything over again basically, but there is some short cuts.
First you will need to just install the SSHD, and install Windows clean to it, then run all the patches onto it, then start to install all the basic 'apps'. That would mean STEAM but >>NOT<< the games (yet), Office Suite, etc.
The riskier way:
Now make sure in BIOS / UEFI is set the SSHD as the default drive to Boot from. Now plug in your old HDD. Copy over from the 'D' drive (the old HDD) to the new drive the game directories, music, movies, etc. DO NOT COPY PROGRAMS this will NOT work! ---> Risk here is BIOS/UEFI will get confused WHICH Windows (C or D) is the REAL one and numerous times can cause the drives to 'reset' or alter the BootSector, making a drive 'blank' and potentially losing your data.
Easier way:
Assuming this is a A) SATA and B) 5 1/4 drive you would need to get a SATA to USB with EXTERNAL POWER adapter. If this is B) 3 1/2" or smaller (i.e. laptop drives) then you can just get the SATA to USB connector only, as the USB port can power the smaller drives only. Once you plug it in, you now will see a D drive, just as described before 'File Manager' manual copy the Data ONLY (Games Directories also). Then when you 'point' to the game through the client (Origin, Steam, etc.) it will just verify the files and not need to redownload all the games.