I use a kitchen colander instead of a net, so they can’t get caught up- works well. I use my specimen cup to scoop them up and then pour the water with fish into the colander over a bucket and plop fish into the tank.
Also, you’ll definitely want to treat... the coming and going of spots does not indicate that the ich is “gone” just that the mucous has faded away from the entry wounds. The spots are a symptom of the parasites, but not the parasites themselves. They can only be viewed via microscope.
Especially with sharks in the tank (they don’t handle treatments well, and you wouldn’t be able to have a true fallow period with them there). I wouldn’t risk introducing the fish until he has been treated and then observed med-free post treatment for 2-3 weeks minimum.