Mass vasectomy is one option being discussed by local councillors seeking humane ways to reduce the size of the herd, which boasts around 60 goats.
The animals are all descendants of a pair of Kashmir goats the Shah of Persia gave Queen Victoria shortly after her Coronation.
They have been grazing the limestone grassland on the 719-acre Great Orme Country Park near Llandudno for more than a century.
It was the local landowner, Major-General Sir Savage Mostyn, who turned two of the white goats loose on the Orme after being given a pair from the Windsor Royal Herd which has supplied the regiment with its mascot since 1844.
Last year, the Country Park working party called for a humane cull of old and sick goats because of a shortage of grazing to sustain a healthy herd that size. But the scheme was scrapped after 5,000 people signed a petition demanding preservation of the entire herd. Now a similar battle looms as Conwy Council seeks a solution to the problem in talks with the Royal Society for the Prevention of Cruelty to Animals and the Countryside Council for Wales.
"Technology is as yet not well enough developed to implement birth control methods through treating female goats, therefore other options are to be considered including vasectomy of males and relocation of animals," said a council spokeswoman. "No decision has been reached as yet."
Christine Jones, the organiser of last year's petition against the cull, who lives in a two-bedroom cottage on the headland, said: "The idea of giving these goats the snip disgusts me because there is no need. I think nature takes care of nature and to talk of a population explosion is ridiculous.
"Ten years ago there were 100 goats on the Orme and there is plenty of gorse and scrub for them to eat. They might go into the odd garden for a change of diet but the goats do nobody any harm. They are beautiful animals - the tourists think they are gorgeous and so do the majority of locals.
"On a moonlit night you can only see their horns when they sit up on the cliff - its just fantastic. We fought so long and hard we thought the battle was over but if they touch the goats without our approval we will take out an injunction against the council."
Complaints have been made by some locals who say the wild goats stray into gardens and cause havoc when grazing is in short supply.
But supporters of the herd point out that the town's Rectory Tea Gardens still manage to win the Llandudno in Bloom contest even though the goats are often seen wandering there.
Sally Pidcock, assistant warden of the Great Orme country park said "Obviously people are sensitive about culling the goats but if you leave them as they are maybe they will suffer in the long run.
"We don't want to get rid of the herd entirely and giving a vasectomy to all the goats would effectively wipe out the herd," she said. "The goats are part of the Great Orme and we don't want to lose them but for the sake of the Great Orme and the goats their numbers should be reduced."