My little Shetland flock escaped, on the same day my neighbour brought loads of his 'big white sheep' up from his main holding, to the fields next to mine. So I had to get mine out from in amongst his flock.
I walked in and rattled the bucket, and called. And a flock of little coloured Shetlands followed me right through the middle of the big white flock, and back into my fields.
So my point is that you don't need halters, to get them out of a mixed field. Teach them that you are the source of all goodies, and teach them a call at the same time. ie go right up to them, sprinkle a bit of tasty food from a bucket and call. Even if you're only a foot away. You're aiming to get the association in their mind between the call and the food. Keep increasing the distance, til you call and they come to you for food, even in the same field. Make sure you don't feed the cows too, you don't want them learning the call=food thing too!
Once you've got that sorted, you can move your sheep out of the field, from in amongst other animals, by shaking a bucket and calling.