Captan is a penetrant. it is that characterisric that makes it problematic in tank mixes.

Yes you can use dish soap. It says so on the directions for Captan. Its in the last page somewhere. It says to use it on plants such as roses that are hard to "stick". Just use a few drops.

The problem with Captan is that like other fungicides with multiple modes of action, it can be phytotoxic to the foliage.

The reason not to use it w/ sticker/spreaders is that they typically have some penetrating action. Captan is generally fine if it sits on the surface of the leaves, it's when it enters the leaf tissue that it can cause damage. A penetrant will carry Captan into the leaf tissue.

Oil is also a penetrant and can cause damage when used with Captan. Oil can even be phytotoxic by itself, so should definitely not be used with Captan.

Captan probably doesn't need a sticker/spreader. It stays on fairly good in rain by itself. When it does wash off, it's noted for its re-distributive properties (i.e. it washes onto new foliage).