First myth to put down: recharging every day.
No, modern smartwatches certainly do not require recharging every day. My $39.99 Blaupunkt BSW9 smartwatch (bought from Supercheap, and super, super cheap it was!) gets a recharge once each
14 days!
I see fancy (and expensive!) smartwatches gracing every wrist that comes into view, mostly Apple or Samsung, then comes the large Suunto and FitBits. Their ginormous size is kind of off-putting; fine if you have arms as big as mesmates, way too imposing attached to a stringbean...
But what if you lose those big watches, or fall and break the glass?
The Tissot analogue watch I wore from 2014 up until this year served me very well; analogue but battery driven, no alarm. The problem at the time and before retirement was I travelled frequently interstate, and got irked from winding forward, back or making adjustments to the time. Nowadays smartwatches get their time cue from either inbuilt GPS or their persistent link to the user's phone — time is adjusted before you remember it! How did we manage without that!?
Like many SWs, the Blaupunkt I have is a blackout e.g. nothing visible until touched, or wrist turned (selectable). Daily steps (stride for walking and running is fully adjustable), distance, type of movement (hiking, walking, running) height, weight, sleep time, calories. Best thing I ever bought from Supercheap (besides spark plugs and polish...).
To go all mechanical with no battery, you probably have to look at bespoke retailers specialising in this niche. Never heard or seen of an all-analouge watch with an alarm function. Daily-Winders do exist, but you'll be paying a premium for a 'backward' timepiece when any of the modern and cheaper (or 6x expensive!) products will do the same thing and provide more information on your activities, if that is what you seek.