The OED gives the etymology of “blunt” as:
Etymology unknown: found in Ormin c1200, in a sense which has
suggested some connection with Old Norse blunda to doze, [but very
unlikely to be so]. Other suggestions are that blunt might be … a
nasalized derivative of a Germanic root blut-, whence Old Norse
blaut soft, weak, modern German blosz naked, Frisian blat, bleat naked, Old English bléat wretched. But in the present state of the
question these are mere conjectures, having no contact with the
history of the word.
The derivation from blut- is attractive in the sense that the blunt comment does not come with any adornment, but it can only be speculation.
In its earliest form, we have no connection with sharpness, rather
A. adj.
1. Dull, insensitive, stupid, obtuse: said, it appears, originally of the sight, whence of the perceptions generally, and the intellect.
(Now generally with some antithesis to sharp)
c1175 Ormulum (Burchfield transcript) l. 16954 Unnwis mann iss blunnt & blind. Off herrtess eȝhe sihhþe. [a stupid man is blunt and
blind …]
[The antithesis to sharp, which is probably a red herring for the purpose of the OP’s question, does not appear for another 200 years:
2.a. Of an angle, edge, or point: Not sharp, obtuse.
1398 J. Trevisa tr. Bartholomew de Glanville De Proprietatibus Rerum (1495) xii. xviii. 426 The capon is more cowarde of herte..his
spores ben made blonte.
Another 150 years gives us the figurative use:
1562 J. Heywood Sixt Hundred Epigrammes lix, in Wks. sig. Ddv Great diffrence betweene blount woordes and sharp swoordes.
However, this does not carry the same idea as the modern “speaking bluntly” – it alludes the real damage that words and swords do. ]
In the late 15th Century, we have
†4. a. Rude, unpolished, rough, without refinement. Obsolete or archaic.
1477 T. Norton Ordinall of Alchimy vii, in E. Ashmole Theatrum Chem.
Britannicum (1652) 106 In English blunt and rude.
a1522 G. Douglas in tr. Virgil Æneid (1957) i. Prol. 314 Thocht
myne be blunt, his [sc. Vergil's] text is maist perfyte.
1530 J. Palsgrave Lesclarcissement 306/2 Blont in maners or
rude—rude.
Only a little later, there is more suggestion that the “naked/without adornment” sense was still in use:
†3. Barren, bare. Obsolete.
1553 G. Douglas tr. Virgil Eneados xiii. vi. 227 The large
planis..Stude blunt [MSS. & ed. 1874 blowt] of beistis, and of treis
bare. [The great plains… stood blunt of beasts and bare of trees.]
And it takes little to see the connection between these two nuances.
At the end of the 16th century, we have what is the current meaning of the word “blunt” in the sense that the OP asks:
5. Abrupt of speech or manner; plain-spoken; curt; without delicacy; unceremonious.
1590 R. Greene Neuer too Late i. 51* One blunt fellowe amongest
the rest that was playne and wythout falshoode, tolde her the whole
cause.
a1616 W. Shakespeare Henry V (1623) iv. vii. 174 By his blunt
bearing, he will keepe his word.
And we see that “without delicacy” incorporates the rude and the unadorned.
The idea of sharp has taken a backseat in the development of the word and should be disregarded.