Glasslover 2015, I don't know of any Davidson catalogue/s that show this particular 'dolphin' design (which was, by the way, unregistered).
The catalogues of Davidson unregistered designs issued between 1880 and 1890 show four 'match stands', pattern numbers 300 through 303. Numbers 300, 301 and 303 have a sharply 'stippled' area on part of the exterior that acted as an abrasive surface against which to strike the heads of non-safety matches. See the attached catalogue images and photos of number 303 match stands in black opaque and purple marbled glass. (By the way, both the 303 match stands are marked with the Davidson demi-lion trademark on the underside of the foot).
Your 'dolphin' piece does have a stippled area to the top of the foot which could possibly have served as a match striker. I suppose the acid test is to try striking the head of a non-safety match against it and see if it lights! - if it does then you have a salt-cum-match striker, if not then you have an open salt.
Fred.