I agree with Bongo except for using MSE. If you are using a different AV than MSE, use that to scan the drive. MSE has been consistently scoring low in AV (anti-virus) reviews. When I tried MSE a while back , I had problems with it, including a couple of infections that slipped through. I prefer the free version of Avast but there are other good ones out there.
Malwarebytes Anti Malware, aka MBAM, is a free scanner that can be used to scan your entire computer as well as an external drive. I strongly recommend it to use for weekly scans as well as whenever you suspect something may not be totally kosher. You can download it from here
Another excellent scanner that can be used with your AV and MBAM is SuperAntiSpyware
(SAS). It looks for spyware and adware which may slip by AVs and MBAM.
Running your old HDD from a dock attached to your new computer will not allow the copy of Windows on it to run unless you set it up to do so. Since malware on an OS sometimes disables antimalware programs, scanning the HDD from a different computer as you would be doing is far more likely to catch any nasties that may be hiding in your data.
When I built my present desktop computer, I simply installed the HDD from my old computer in the new one, scanned it for nasties, then copied the data from the old HDD to a new one in the computer, taking the opportunity to reorganize it as I went. Once I was satisfied I had all my data transferred, I then wiped the old HDD and kept it in the computer for future expansion since it was still in good condition. You can do the same by using a dock.