I've copied many files with Knoppix, and know of no reason why you would not be able to copy exe files. I have copied many exe files with Knoppix. Of course, you face the normal Microsoft file system restrictions when you use Knoppix, you can't copy a file over 4 gig in size to a FAT partition, for example. And if copying from a Win98 fat partition you many need to drag and drop or use the 8.3 format filename, not copy by name a long file name with spaces or other special characters in it. I generally avoid software with absurd DRM functions built in, but I don't know of any windows programs that do anything to an exe that would make it difficult to copy. Some certainly might hide extra hidden files on the system, or make registery entries that the software will not run without, so just moving an EXE to a new computer often isn't enough, but I have not seen an exe that couldn't or shouldn't be moved.

Of course, since you were having system problems already that you needed Knoppix to aid recovery for, you might actually have had some disk problems that made reading some sectors hard. But it doesn't seem likely that such a problem would only affect exe files, unless it hit a portion of the disk that Windows just happened to select to load the exes to.