Hi, what's more important (than styling for now) is getting it into fast draining grit, and allowing it to mostly dry out between waterings, though if you keep it outdoors for the summer then you'd have to water more often, especially in the grit. Don't strip anything yet and while a somewhat shallower and wider pot is a good idea, there's no rush as bonsai pots slow growth, and you want more now to give you more to work with when styling.

According to the website I've linked to, a bonsai of a schefflera requires even, consistent watering. This site grows and sells schefflera on lava rocks. I've got a couple and they are really neat.

Here is a link that might be useful: fuku bonsai link

Well, yes, if you grow anything on a rock, in Hawaii, you need to keep it watered properly, but the majority of us who get our trees in supermarkets, take them into cold and dark (relative to outdoors in Hawaii) homes and stick them in potting soil have very different experiences. If we kept them 'well watered' they would be dead in 2 wks.