Bludgeon is a short, heavy club which is thicker or loaded at one end.
Both OED and Etymonline say “origin unknown”. There are possible Cornish, Celtic, Dutch, cant, Middle French, Irish and Gaelic origins suggested in various sources.
OED mentions the possible Cornish, Celtic, Dutch origins and the connection with blood:
Not found before the 18th cent.: origin unknown.
Blogon (with g = j) is quoted by Dr. Whitley Stokes from the Cornish drama Origo Mundi (? 14th cent.), but its relation to the English is uncertain. Other Celtic etymologies sometimes proposed are on many grounds untenable. A Dutch verb bludsen to bruise, has also been compared; and it has been suggested that the word is of cant origin, connected with blood.
In OED, the first citation is from a dictionary also:
1730 N. Bailey et al. Dictionarium Britannicum Bludgeon, an oaken stick or club.
Wiktionary mentions the Cornish and Middle French origins:
First attested in 1730. Origin uncertain, perhaps of Cornish origin (recorded as blogon c. 1450) or from Middle French bougeon, a diminutive of bouge (“club, stick”).
The Concise Dictionary of English Etymology (By Walter W. Skeat) mentions the Irish and Gaelic origins:
a cudgel. (C.) Irish blocan, dimin. of ploc, a block; Gael. plocan, a mallet, bludgeon, club, dimin. of ploc, a block; W. plocyn, the same.
Is it possible to trace back further and/or find a more definitive answer/source?
The OED’s citation of Nathan Bailey, Dictionarium Britannicum (1730), mentioned in the posted question, seems to be off by one edition and six years. I checked my print edition of the full OED, and it does indeed cite the 1730 edition of Bailey’s dictionary. But that edition of Bailey’s dictionary has no entry between
To BLUBBER, to cry or foul the cheeks with tears.
BLUE a colour well known.
In contrast, the second edition of Dictionarium Britannicum (1736) has this entry between “BLUBBER LIP’D” and “BLUE”:
BLUDGEON, an oaken stick or club.
About 20 years later, Samuel Johnson, A Dictionary of the English Language (1755) has this entry:
BLUDGEON n. s. A short stick, with one end loaded, used as an offensive weapon.
Although the OED seems to have misidentified the year of the first dictionary entry for bludgeon, I found two instances of bludgeon in the wild that really are from 1730. From The Grub-Street Journal (January 8, 1730):
Tuesday, Jan 6 … Last Sunday Night about eleven o’Clock, Mr Stalton the brewer, was attack’d neat the end of Thrift street, Sobo, by a single Vilain, who pul’d out a Bludgeon, and knock’d him down, and then rifled him of his Gold watch and Money, which Mr Stalton believes to be upward of 12 l and then made off, and yesterday he was seized offering Mr Stalton’s Watch to pawn, and being carried before a Magistrate, was committed to New-Prison.
And from The Political State of Great-Britain (March 1730):
The wicked People that carry on this inhuman Trade of knocking People down thus, before they rob them, or so much as ask them for their Money, are observed to do it with an Iron Bar or Truncheon, which they call a Bludgeon ; which is about two Foot in Length, and is carried under their Cloaths, by which they give such a desperate Blow on the Head, as several have had their Skulls broken with them, and have never recover’d the Injury of it; and it is observable also, that the Women carry these cruel Weapons about them as well as the Men, and perhaps use them the more cruelly also of the two.
This last instance suggests that bludgeon may have originated in English as street slang; however, it doesn’t appear in any of the dictionaries of English slang from the eighteenth and early nineteenth centuries that I consulted.