Both breeds are on New Zealand's list of critically endangered animals.
There is a 0.3ha sanctuary for skinks near Alexandra, and the trust, with the Department of Conservation (Doc) would like to extend it to 14ha for the purpose.
They are investigating, with fencing specialists, a more affordable fence to keep out predators. The fence design is inspired by one that protects takahae in Burwood Bush, near Te Anau.
The new fence is expected to cost $80 a metre, $370 a metre less than the existing fence.
Doc officer Tim Whittaker said the new fence would be 1.8m high, lower than the old fence.
"The older fence is more robust and has a metal cap.
"The new one has a front face with a plastic skirt and an overhanging net which will stop cats jumping over," he said.
The new fence would exclude all pests except mice but Mr Whittaker said research had shown "grand and Otago skinks will survive if pests are taken down to a low level, which has allowed us to look at cheaper fence options that may not be 100% predator proof".
The trust would deal with any mice that got into the area. Mice were most difficult to keep out because they could squeeze through a hole the size of a pencil.
Fine mesh had been used on predator fences "but joins or any minor gaps that have developed over time have let in mice".
The trust would build a 20m trial fence to test the design before committing to the full 1600m fence. It hoped to build the full fence in summer or next autumn but that was dependent on trials and funding.
The trust was considering funding options, its chairman, Grant Norbury, said.
