ISBoxer 36 or later

There is a new option in ISBoxer 36 to set the console hotkey through your Character Set, labelled "In-game Inner Space console hotkey". If the box is unchecked, the default console hotkey is used, which is ` if you have the key, otherwise F12. To disable the key binding entirely, check the box and leave the hotkey blank (or select <NO KEY>). To change it, just check the box and set a hotkey.

ISBoxer 35 or earlier

To disable or change the console binding:
1. Right click the Inner Space icon in system tray, and select Configuration
2. Click "Startup" underneath "Session" in the upper right corner
3. In the list that comes up on the left, click "Console"
4a. If you want to just disable the Console binding, click Remove
-- or
4b. To change the Console binding, see the command on the right hand side. It says "bind console ` console toggle" (note: for keyboards that do not have a ` key, this will be F12 instead). You can change it to, for example, alt+`, i.e. "bind console alt+` console toggle". If you're trying to get creative with the binding, the names for all the keys are the same as listed in ISBoxer in any Hotkey Picker window. If it has a space, put quotes (") around the entire combination, i.e.:  bind console "num lock" console toggle.
5. Click Apply

Changes will take effect when launching a new game instance.