saw a similar one on a google search, no dimensions tho.
3in. grip on yours is short, as noted maybe it broke off and was field repaired at that length?
in the 1800's they went to a larger, longer standard pattern middies dirk with a back strapped rayskin grip. prior to that it would have been a private purchase item of various size and quality depending on the new officer's purse. the midshipman's ages varied from pre-teens to grey haired and bitter men who had failed their exams for promotion to lieutenant. stuck halfway between the common ratings up forward and the real ossifers aft they were truly mid ship men.
this one attached from google images was noted as 1750-1770 british naval dirk, it appears to have a similarly etched blade too. it is missing the black bands of grunge accumulated in the grooves on the one in post no. 1.