Learn English – Does “This blows!” (it’s bad) derive from “This sucks!”

I would say it has onomatopeic roots.

Firstly, this isn't the only word for masturbation to have echoic roots: fap is echoic of the noise of masturbation.

Looking at the entry in the OED, some of the uses spell the word whank, and in fact one example mentions that it might be echoic:

1951 E. Partridge Dict. Slang (ed. 4) 1220/1 Whank, (male) self-abuse: low: from ca. 1870. Perhaps echoic.

Looking through Google books, it shows that whank is used as echoic of bird calls:

For example

"Whank, whank, whank!" the little bird calls.

Also in the wank form:

"Wank, wank, wank", it trumpets, in a musical, nasal tone

Given that the OED's earliest citation (1948, British RAF) refers to a bed, I would think that wank is echoic of the sound of bed boards or mattress springs.

Your question was actually the subject of a paper: Minge --- A Loanword Study by James Clackson. Clackson asserts that minge is, like pal, nark, and lollipop, a loanword from Romani Gypsy. While the OED dates the first use of minge in text as 1903, it had been used since the 19th century in (very) informal conversation --- it belonged almost solely to spoken English, and even then, appeared to have been commonly used only by speakers of certain dialects.

However, to complicate matters, the origin of minge in the Romani language itself is somewhat uncertain. Clackson suggests that it came into the Romani language as a loanword from Armenian.

The origin of minge is rather interesting --- I suggest you read the paper. It should adequately answer your question.