This is not the time to use parallelization. You want the files to go together in a defined order, and the same order. Parallelizing could make separate bits go in front or behind each other. Asynchronous processing will cause nondeterministic resource allocation.
Also: you won't get much speedup because 'cat' doesnt use a lot of CPU, you're already bound by the speed of the disk drives, so accessing them multiple times is a detriment.
You could fix both issues with a binary tree system. Doing pairs and working up to a complete picture. It's more effort; worthwhile if you do this task repeatedly. Let the operating system and RAID drivers handle that kind of parallelization. With regards to the userland application, a single "cat" will dump the datafile as fast as possible.