I haven't found any serious attempt at an etymological explanation for the term cheatercock. The older Indian sources I checked don't suggest that there is any sexual innuendo involved in it. For example, from Samyuthka K, "Indian English," in the Times of India (April 23, 2016):
Cheater cock!
No, this doesn’t mean that he was in someone else’s pants. This gender-neutral phrase means someone cheated in an exam or just lied about something!
I suspect, to the contrary, that the implication is that the person cheating is doing so in a brazen or ostentatiously unrepentant manner, suggestive of a strutting rooster.
The oldest match for cheatercock that Google Books search turns up is from Malaysia, not India—although evidently spoken by an ethnic Tamil character. From an unidentified story in Lloyd Fernando, Malaysian Short Stories (1981) [combined snippets]:
Ali's top was also a new one, but it was not as beautiful as Chranpal's. Kanda's top was a good one. It was full of pock marks where pieces of wood had broken off after it was hit. But it was still in one piece and Kanda believed that his was the magic top that couldn't be broken. Rama's top was in good shape, and it really had a strong nail and Chranpal was afraid of it.
"OK, let's start," said Kanda.
They cleared the dust again, cleaned out the hole , made a circle and started. At the word "go", the four boys began to string their tops. Rama was the first to swing, next Chranpal made a throw, Kanda's string got loose and he was the last and he had to "pasang" the game. He placed his top in the middle of the circle.
Rama attacked with his top. It hit Kanda's but did no damage. Next Chranpal threw in his and it just grazed Kanda's and Ali's top didn't hit Kanda's at all. They played on and soon Ali had to "pasang" his top.
Chranpal tried to play a careful game. He wasn't as powerful a player as Rama, but he wasn't too bad either. He tried to steer a middle road. He did not try to put in too much force in his throws when he was hitting Kanda's and Ali's tops , hoping they would also show mercy on him. But Rama was ruthless. He swung his arm and his top would send the others flying. Chranpal waited his turn for "pasang" with fear. "Oh God, please don't let me be out," he whispered.
They played on. Chranpal's mother came out and called to him to come home, and he felt that he should seize the chance and run home. But the other boys would not let him go.
"You don't be a cheatercock, eh," said Rama.
Chranpal couldn't do anything and he yelled back to his mother, "Wait, I am coming," and continued playing. He knew that his turn for "pasang" would come and he just wished that his top would not be broken. That they would somehow spare it. If he got through the "pasang" then he could go home honourably without the others calling him a coward.
It may be significant that cheatercock arises here in the context of a children's game of battling tops, given the fact that (as Laurel points out in her answer) fighting cocks (roosters) is a centuries-old pastime. If the term originated in the specific context of battling tops, the inclusion of "cock" in the term might be a pejorative comparison of "cheatercocks" to honorable fighting cocks. There is very little information to base such a specific origin of the term on, however.
None of this is to say that nonsense-sounding words ending in -cock can't have a sexual component. One famous instance occurs in act 3, scene 4 of King Lear, when Edgar, in his guise as Tom o'Bedlam, chants, "Pillicock sat on Pillicock-hill. Alow, alow, loo! loo!" Alexander Schmidt, Shakespeare Lexicon and Quotation Dictionary, third edition (1902) offers the following gloss on pillicock:
Pillicock (Qq Pelicock) a term of endearment, with a lascivious double-meaning: Lr. III 4, 78 (alluding to an old rhyme: Pillicock, Pillocock sat on a hill: if he's not gone, he sits there still).
The OED, with rather less delicacy, offers the following entry for the word:
Pillicock. Obs. ... {f. pill, also pillie and pilluck, all north. dial., = Norw. dial. pill (Aasen) penis} 1. The penis (vulgar). [Citations omitted.] 2. 'A flattering word for a young boy'; = 'my pretty knave' (Cotgr.).
Like any -cock word, cheatercock is susceptible to a phallic interpretation by readers or listeners who are that way inclined, but I see no reason to suppose that it originated with any such signification in mind.