Can you control Tonic without using the mouse or trackpad?

Yes, you can control the Tonic Pad Player without using the mouse or trackpad.

The Tonic Drone Presets are designed to be chosen in advance. You can use a two finger swipe on your trackpad up/down to switch between them. You can also assign any midi control to the drone preset box while in Layout mode, and a second knob to the drone center if you do want to make changes on the fly.