Here's one that we haven't talked about yet: the laser scalpel from mid to late TNG. It was also briefly used as a dermal regenerator / suture. The prop was most visibly used during the surgeries in "The Host" and "Ethics," and in "Frame of Mind" to heal Riker's temple wound (more in a suture/dermal regenerator manner).
The most unique name this has is Exoscalpel, from "Ethics," so I propose that's the best name given how many other dermal regenerators and laser scalpels there are.
The Host, 4x23 "laser scalpel"
In Theory, 4x25, sitting on table in background
Disaster, 5x05, used to cut Molly O'brien's umbilical cord
The Game, 5x06, used to disable Data
Ethics, 5x16 "exoscalpel"
The Perfect Mate, 5x21, on table in background
Frame of Mind, 6x21
Note that a slightly larger version of this was built for DS9 as an engineering tool and could be found in O'brien's tool kit:
It's largely similar in shape, apart from the size and trigger button being different.
The TNG version apparently did make its way to DS9 as well, though, according to Ex Astris:
The Alternate, 2x12
Blaze of Glory, 5x23 (gold tape added?)
I also noticed what appears to be the tip (though it may be from the larger DS9 version) sitting on a table in a Voyager screenshot: