Please note that melee weapons are affected in the mystery pick as show here:
https://www.reddit.com/r/fo76/comments/dctfrg/psa_melee_for_mystery_pick_is_screwed_up/
Hey thanks for sharing this bug report. Due to the issue that was affecting Mystery Pick melee weapons, we've replaced this weekend's Mystery Pick event with a 25% off Purveyor Sale Event.
The sale will last the same amount of time as the Mystery Pick would have, until 12pm ET on Monday, October 7. Full details are here on our forums.