Green’s Dictionary of Slang

blue-veined adj.

[blue vein n.]

in combs. referring to the penis.

In compounds

blue-veined diamond cutter (n.)

the erect penis.

[US]Simon & Burns ‘Ebb Tide’ Wire ser. 2 ep. 1 [TV script] For your information I wake up every morning with an angry blue-veined diamond cutter.
blue-veined havana (n.) [SE Havana (cigar) + smoke v.3 ]

the penis; thus smoke the blue-veined havana, to fellate someone.

see blue-veined custard chucker
‘MillenniumJazzman’ ‘Rev. of Topless Room Service’ on DVDPornReviews [Internet] She deep throats him, spits on his cock, slurps it, licks it, sucks it and totally dominates his blue-veined Havana until he is a fuck puppet at her mercy.
blue-veined hooligan (n.)

the penis.

[UK]P. Meditzy ‘A Day In The Life Of...’ 29 Apr. [Internet] My ‘blue veined hooligan’ had been getting a bit sore lately.
blue-veined junket pumper (n.) (also b.v.j.p., junket gun, purple-helmeted junket gun) [SE junket, whey + pumper]

the penis.

[Aus]B. Humphries Barry McKenzie [comic strip] in Complete Barry McKenzie (1988) 125: Clean-living churchgoing tinted nurses [...] who probably know a few tricks with a B.V.J.P.
Allan & Burridge Euphemism and Dysphemism 100: The blue-veined junket pumper is a rather picturesque, even poetic, term for penis.
[Aus]B. Moore Lex. of Cadet Lang. 203: junket gun the penis. See purple-helmeted junket gun.
blue-veined piccolo (n.) [SE piccolo]

the penis.

see blue-veined custard chucker
Spleen ‘The Spinal Column’ in Japanzine 11 Issue 4 [Internet] I knew it was the real Yoshi even without seeing his blue-veined piccolo.