Is there any battery-less Android-based device
Don't you worry. LiIo batteries are not that concerned about that. What really lowers their life span are "complete discharges", not frequent "trickle-charging". It's even recommended to charge them as soon/often as possible (and practicable, of course).

See e.g. Wikipedia: Lithium Ion batteries for details, and also take a look at our question Does constant charging harm my Android cellphone? and its answers.