Fortunately, in the quest to devise a product for every possible application, shoemakers have come up with a pretty substantial number of products that perform like aqualung-equipped trail runners. In general, the idea is that they have sticky soles for traction on wet logs and rocks (although there are limits to this); enough support for walking without feeling like boots; drain holes so that water can get out as you transition from the river to the trail; and water-resistant, fast-drying materials that can take repeated soakings.
A good example of this genre is the Salomon Tech Amphibian ($85; www.salomonsports.com), which has all the requirements listed above. This pair even works well with Neoprene socksthe back of the shoe collapses so it can be worn like a slip-on. Or, lace the shoes up for extended walking. Teva's Rodium shoes ($80; www.teva.com) embrace a similar concept, with a sole designed for especially good traction on slick surfaces. Adidas' Hellbender ($90; www.adidas.com) is a shoe I like, having worn it over the past yearlike the Tech Amphibian, it's sort of a modified trail runner, and I've found it to be very stable for a low-cut shoe. As a bonus, REI has some sizes of the Hellbender on sale for $60.
Nike is in on the action, too, with their Toketee Mid ($60; www.nike.com), essentially a Neoprene sock with a water sandal wrapped around it. It skews a bit toward the "water" side of things, as it's a little soft for extended portaging, but it has adequate support and good foot protection for dry-land use, with good insulation for long wet periods.
So there you go. Any of these shoes should do a great job for you.