I don't think it's a tremendous safety issue at all. Some points that matter:
--same exact bullet diameter
--max pressure spec for the .380 is quite a bit lower than 9mm
--brass case will not need to be forced in to a 9mm chamber as it is smaller at the case head
Those items relate to the "safety" of doing this. However, back in the real world, this is a pretty senseless thing to do. Ends up being a losing proposition for a number of tangible reasons.
.380 ammo is simply more costly than 9mm ammo all across the board on comparable products. Simple economy of scale. While it's true you're talking about leftover ammo that is long-ago paid for and costs you nothing now, you're talking about a half a box to be shot up in a very expensive revolver for which it was NEVER intended.
Given the lighter bullet and the lower pressure, it's very doubtful that it will even shoot to point of aim. You could theoretically adjust the sights... but for the purpose of a half box? So we're left with this as a purpose:
--to see if it will work
--to make a "bang" noise
--to remove clutter from your world in the form of a half box of ammo
I compare it to this...
I could find a wood dowel that fits the bore nicely, prime a single case, load it, cock the revolver, drop the wood dowel down the bore and then discharge that primer with the expectation that the dowel would be launched from the handgun at "some" velocity and it most likely wouldn't harm the revolver and if pointed in a safe direction with a quality back stop, also would not be any sort of safety issue.
However...
Why would I do such an exercise?