The OED lists the adjective as pre-launch.
Collins lists same as prelaunch.
And you have already posted MW's spelling.
My sense is to use either, but if you hyphenate one (pre-launch) hyphenate the other too (post-launch). Same for using no hyphens.
Even prelaunch can be found hyphenated and UN-hyphenated!
And pre is a preposition: OED
previous or prior to
Post can be a preposition in sense too.
Thus, the following would be correct:
… through the pre and post-launch process … (your example - without the hyphen)
… through the pre-launch and post-launch process …
… through the prelaunch and postlaunch process …
… through the (pre, pre-launch, prelaunch) and post-launch (postlaunch) process …
And finally in a sentence:
During the launch process, both pre and post, the aberrations in X