I've also been looking on many rescue sites in Scotland and they seem to be full of bull terrier and collie types, I think small dogs are snapped up really quickly. But I don't think you'd go wrong with a Shi Tzu or a Lhasa
If it’s anything like a lot of the rescues in the NE of England, the rescues will have waiting lists for both certain breeds and also “type” of dog and so they never make the websites. Only the staffie / lurcher / collie type dogs often don’t meet anyone’s criteria on the waiting lists so are the ones you see advertised.