Definitely tune that. The file-system is probably working in 4KiB blocks so there would be no benefit in working on smaller ones. In fact as you'll write to each block four times you are probably wasting a lot of time and causing more wear than you need to.
I would suggest something far bigger (in the MiB range at least), especially on traditional drives where reducing head movements is key but random access latency on SSDs is not as close to zero as many people think particularly for small writes. Make sure that whatever you move the data with is loading that full block of your desired size into RAM before starting to write to the destination (i.e. perhaps pipe through something like "buffer -s 4M" if your read/write tool of choice does not support this directly).
In fact an SSD might internally be working with MiB sized blocks, another reason to work in that scale at least and be careful of alignment where you can detect it or the lack of it.
But yes, that solution would definitely work if carefully optimised.
> The correct solution, of course, is to buy a second disk.
Definitely. Must faster, and you still have the original data in-place so you can run checksums to verify the new copy before committing to use it.