I can see why no shearer will come

They expect the sheep to be penned and ready to shear when they get there, not to have to chase them up hill and down dale. Soay usually self-roo ie their fleece will come off by itself, but from what you say it sounds as if they have three years of fleece on them.
You have three months before shearing time to try to tame them. The usual way is to tempt them in with food, but as we are past the worst of the winter that might not work, if they are unused to being fed. I have written a fairly long piece somewhere on TAS about how to do that. How do you get them in to worm them and treat them with anti-flystrike stuff?
A dog is unlikely to be able to work with them if they are that flighty and the dog is not used to working with Soay - they will just scatter and sail over your fences.
I once had to help my brother to catch his wild flock of Manx Loughtans - which weren't as wild as your Soay sound. We got them into the smallest field then got lots of people with a 50m length of electric netting (not electrified) and went fishing

We chose a corner where they couldn't jump over, herded them quietly into that whilst making the net smaller and smaller, then eventually threw the net over the lot and each person grabbed one and hung onto it. Far from ideal but it worked - twice, once for shearing then later to send the devils off to the abattoir.
I am a great fan of Soay, but if they run wild (which ideally they should to preserve their wild characteristics) then management becomes near impossible.