The answers stating that the risk is basically 0% are completely correct.
However I would add one thing to
Would the same answer be for SSD copying?
As said in the top answer, both HDDs and SSDs do have a very much more relevant wear-induced failure risk than CPUs do. The failure modes are quite different:
- HDDs wear out from changing position. This happens on both read and write operations, but is minimised by changing large amounts of data in one uninterrupted batch. So, copying the entire contents is about the most wear-friendly way you can access a HDD.
- SSDs (flash-based ones, that is) don't care about reads (whether sequential or random-access), but wear out from write operations, and that at a somewhat constant rate. You'll find very different figures about how many write cycles a flash cell can endure, ranging from 100 to 1000000. Also the actual failures are stochastic, meaning some bits can fail quite quickly while most of the rest are still good. As a result, in particular cheap SD cards have a tendency to fail quickly aften being written only a couple of times.
Decent SSDs will have error-detection and block-remapping algorithms that can avoid any catastrophic failure for a very long time, but it is still limited, in particular if you're going to write over and over and over again.
The conclusion is that what you should not do is to copy data from a HDD to another by first copying part of it onto a flash storage, then to the target HDD, then next part to the flash and so on. Like, for example, if you have only one USB port and connect HDD A, copy to laptop, connect© to HDD B, connect again A...
Practically speaking, even this would only matter if you either have a truely huge amount of data (petabytes), or use an underpowered flash medium as the intermediate storage.
If you would need to copy with intermediate storage, a HDD would be the better choice for that, because batch copying is what it's best at.