The hedgehogs are housed in a shed where they are treated for ticks, fleas and internal parasites.
"The conservation charity doesn't want the care they have taken looking after the hedgehogs to be in vain, " she said.
The hedgehogs have been eating birds' eggs and chicks, leading to a big decline in the population of rare waders.
The cull is due to resume next spring, but SNH said it was still willing to hand over the hedgehogs it caught to animal rescuers if it could be scientifically shown that they can survive re-homing.
An aim of the study is to better understand the part hedgehogs play in the decline of the birds.
BBC: Hedgehogs may have returned to cleared areas of Hebrides
However, now the healthy hedgehogs will be taken to sites identified specifically as being "hog-friendly".
"Shepreth is really struggling financially and one of the biggest burdens is the hundreds of hedgehogs we get in the winter, " she said.
"One of the biggest burdens is the hundreds of hedgehogs we get each winter, " Miss Willers said.
The Wildlife Aid Foundation (WAF) in Leatherhead is concerned it could reach capacity if the anticipated 300 hedgehogs are brought in.
Data collected would provide "essential scientific evidence of the unknown survival and breeding success rates of hedgehogs rehabilitated at the centre", the charity said.
"We feel that we are duty-bound to help all the injured and orphaned hedgehogs that we can, and to get them back out into the wild next spring when they are able to fend for themselves, " Mr Cowell said.
The charity said there are more than 2, 500 hedgehogs in wildlife hospitals around the country.
Then there will be a chance for everyone to sit down and focus on the real issue, which is not whether to kill or translocate hedgehogs, but to see how to improve the breeding success of the dunlin and ringed plover on the Uist islands.
Sick hedgehogs and abandoned baby hedgehogs are brought into the park from across the region.
The park currently takes in about 50 sick, injured or abandoned hedgehogs and hoglets, usually brought in by members of the public.
Hedgehogs were introduced to the Western Isles in the 1970s and efforts have been made over the past decade to remove them from North Uist and Benbecula.
BBC: Hedgehogs may have returned to cleared areas of Hebrides
It is hoped the tiny equipment can be attached to several hedgehogs later this year.
"Hedgehogs are having second litters because of the warmer autumns, " she explained.
Anybody using roads around the UK is asked to take note of how many hedgehogs they see - dead or alive - on stretches of single carriageway roads, on journeys of 20 miles or more.
BBC: NEWS | Science/Nature | Hedgehog numbers 'in nose-dive'
Hedgehogs are suspected of having returned to areas of the Hebrides where they had previously been removed from, Scottish Natural Heritage has said.
BBC: Hedgehogs may have returned to cleared areas of Hebrides
She added that research indicated hedgehogs were dying out at a rate of one fifth of the population every four years.
Since then, flora has sprung up along the embankments, ballast, bridges and walls, creating meadows, wasteland and wooded areas in which a vast range of animals live: there are 220 species of plants and animals, including bees, butterflies, toads, hedgehogs, French oaks and sycamores, and 21 bird species, including the endangered spotted fly catcher.
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