The simplest way to get rivers only where you want them is to export the rivers as a separate image and then composite that layer river on top of your main image using a tool such as Photoshop. You can trim out as many rivers as you want that way. To get old canyons, do an incise flow step with a higher Amount value and a blur of 0.5 to 1.0; a slight precipiton erosion step afterwards can ease the canyon edges.

There is no explicit "keep this as a river" operation. Rivers are an emergent property of the landscape. One way to enforce a river channel is to make three masks: one with just the river, one with your terrain above sea level, and one with the terrain that leaves out the river so that the river looks like an extension of the ocean area. Load the river mask as a selection and drop the altitude in that area by some amount that ensures that a canyon forms. Then load the terrain mask and perform precipiton erosion. The erosion step will allow the river canyon to etch itself into the surrounding landscape without too much artificiality. If you have one, load a solid terrain mask (without the rivers masked off) and then run one more round of precipiton erosion. This last round will remove any hard edges from the canyon masking. This process is discussed in one of the "Fun With Wilbur" tutorials.