MarkB
Legend
I knew the blaster was familiar and thought it was the one Cassian gave him, but I couldn't remember if Vel had any reason to recall it.(I edited this into the previous post right as you were asking the question.)
The blaster is one that Andor got off of Syril way back in episode 3 of the first season. Andor brought it to the Aldhani heist, then stashed it on Niamos in his room at the resort, then after he and Melshi escaped the prison and found their way to Niamos, Andor gave him the blaster.
And yeah, as MarkB said, Melshi ends up in Rogue One (and shows up in a comic book, apparently, between Andor and Rogue One).