A rechargeable (via USB) wireless keyboard with an attached wired mouse.
No batteries in the mouse to run flat. Plenty of space in the keyboard case for a big Li-ion battery. The mouse is small and lightweight.
Does not seem to exist.-- 8th of 7, Feb 23 2018 Something maybe better... https://en.wikipedi...otovoltaic_keyboardAppears to have a built in backup battery [Vernon, Feb 24 2018] The most still has a wire though. That's annoying. Keyboards I don't mind if they have a wire, since they move around maybe 2 inches in a typical week. Also, I have a wireless mouse. It has 2 AA batteries (more correctly 1 battery consisting of 2 AA alkaline cells) that have so far lasted a year. It is noticeably heavier than a regular mouse. I don't mind this. Actually, some gaming mice come with lead weights to personalize the mouse. If light weight is needed, Shirley a small lipo, say an 18350-- bs0u0155, Feb 23 2018 [+] because I wanted one of these a decade or so ago.
It's possible doable without being a commercial product. Starting with a rechargeable,wireless keyboard, a r,w mouse and a USB cable :
1) remove battery from mouse
2) plug usb cable from keyboard to mouse.
Or, you could use the same setup, but have a powered, induction mousepad, which would save having to recharge anything.-- FlyingToaster, Feb 23 2018 // powered, induction mousepad, //
Mouse graphics tablets using semi-passive wireless mice are Baked.-- 8th of 7, Feb 23 2018 I had a Microsoft wireless mouse. It has slots or 2 AA batteries, but I found that it worked just fine with only one. That made it a much more comfortable weight. I have no idea if any other models will do that.-- scad mientist, Feb 24 2018 They don't have this?
Maybe they think "If it's wired sometimes why not leave it wired all the time?" to which I would say "Can't you say that about anything that's rechargeable?"-- doctorremulac3, Feb 24 2018 random, halfbakery