I've been doing the lockdown clear out of tech and cable boxes, and found an old Nvidia Shield Portable with a thoroughly smashed screen. Attached to an HDMI TV it charges and boots up happily enough, and seems like it'll be a perfectly functional TV box, but without a touchscreen I'm not sure what the best options are for controlling it.

Connection options are HDMI mini, a standard wifi network, probably bluetooth, and one USB micro socket that is OTG capable but also the only way of powering the device. It also has a working game controller built into the base unit that could maybe drive a virtual mouse?

Edit: u/mahdif62 has pointed me towards AppGround IO's Serverless Bluetooth Keyboard & Mouse app, which allows an android phone or tablet to operate as those generic devices. Problem solved at a cost of three quid for the pro version. (It's a paid app, the free version is just a very basic functionality demo.)