Your fear about possible data corruption from using a dedicated hard drive case may have merit. I say that because I've seen my fair share of help forums where a drive that worked one day didn't work the next using a USB connection of some sorts. While just putting the HDD in its own case shouldn't cause any issues, I think it might be something to do with the chipset in the case its self and Windows will then render the drive unallocated. So with that, and to be extra sure this doesn't pose an issue, out of abundance of caution, I would make sure you did your research and buy a good, reputable HDD case. I would also backup the data on that HDD just to be absolutely sure.
Again, this shouldn't be a problem, but I've seen it happen. I use a 2.5" HDD case myself and have had no issues. But then again, I used the case straight away and not going from the USB/SATA route to the case.
When you compare reviews on HDD cases and find yourself at Amazon, use fakespot.com to get a grade on the quality of reviews. This isn't a grade on the product. This is a grade on the reviews on whether the reviews can be trusted or not. My rule of thumb is that if a product has less than a C grade I'll look for a different product. I also compare and contrast reviews from more than one site. So from say Amazon to Newegg to even eBay if they have the reviews. Also note that YouTube videos may be by reviewers who have been paid by the company to praise a product. So do your best to judge whether a YouTube review is unbiased or not.
Since I don't trust one single backup, I make multiple backups so that you don't have a single point of failure. I also check those backups and make sure they work.