Conservation body Scottish Natural Heritage (SNH) has decided to discuss its plans with other animal welfare groups and hedgehog societies before going ahead with a cull.
SNH said it would look again at the possibility of moving the animals to the Scottish mainland.
However, a cull has not been ruled out and the issue is likely to be considered again at a board meeting next month.
The hedgehogs have been eating birds' eggs and chicks, leading to a big decline in the population of rare waders.
A handful of hedgehogs was first introduced to the Uists in 1974 to help control slugs and snails in an islander's garden.
Their numbers have grown to an estimated 5,000 in the intervening years.
SNH is the body charged with the conservation of the country's wildlife, habitats and landscapes.
It said the animals were having a devastating impact on the islands' internationally important populations of wading birds - like the dunlin, lapwing, redshank and snipe - by eating their eggs.
Various methods of managing the hedgehog population have been considered, including sterilisation and contraception, or capturing the animals and moving them to the mainland.
However, SNH board members have been advised that total eradication is the only viable option.
"The problem is that we have the most amazing communities of ground nesting wading birds," said George Anderson of SNH.
He said there were about 17,000 pairs in the early 1980s, but that number had halved since then - with some species declining by 60%.
"We have gone from seven hedgehogs to 5,000, so if the hedgehogs keep going up and the bird numbers keep going down it is fairly obvious what is going to happen," he predicted.
The decision to postpone the cull to allow for further consultation was taken at an SNH board meeting in Perth on Tuesday.
Animal rights groups have warned that SNH could face legal action if its board agrees to a cull.
Fiona Stewart, of the British Hedgehog Preservation Association, said there was no need to kill the animals.
"The alternative is to relocate the hedgehogs from the island to the mainland," she said.
'More humane'
She said she believed the proposal was down to money as it would be expensive to relocate the animals.
However, Mr Anderson said money had not been an issue.
"The welfare of the hedgehogs is of prime consideration to us and we feel that it would be cruel to the hedgehogs to do this," he said.
He said those being moved would end up somewhere already populated by other hedgehogs, who they would have to compete with for food.
"That is going to harm the hedgehogs we move and the hedgehogs that are already there," he said.
"They will die slowly, so we feel it may be more humane to cull them here on the Uists."
SNH has been urged to consider exporting the hedgehogs to the south of England by Liberal Democrat environment spokesman Baroness Miller of Chilthorne Domer.
She told the House of Lords: "English gardeners are crying out for hedgehogs to predate on slugs, which are an enormous problem in a wet summer like this."