I haven’t tested this, but Inclusive Technology, a supplier of assistive tech for special education, has introduced the $260 AMAneo BTi, which it says is the “world’s first mouse adapter for iPad or iPhone.”
It purportedly nables users to operate an iOS device directly with any mouse or assistive mouse, including track ball, joystick, head mouse, thumb mouse and more. To use this adapter you must plug in your mouse of choice and connect it to your iPhone or iPad using Bluetooth. A touch pointer will automatically appear on your device's screen.
There are no additional apps to install, so it's very quick and easy to set up, according to the folks at Inclusive Technology. The AMAneo BTi charges using a Micro USB and lasts for up to 20 hours of operation.