What to use for under cabinet lighting for work area without rewiring?

You could use battery powered lights if you have no electricity in the area. There are lots and lots of them available that just stick up under the cabinets. Buy the big pack of batteries and you're set.

There are also lots and lots of LED puck lights available. If you have a place to plug in a lamp you can use those. They use a small transformer that plugs into the wall and uses little power.

Use battery powered.

Christmas rope lights, which are now sold all the time. Or the self-stick battery

puck lights.

I just saw one from Black and Decker... advertised on both DIY network and on HGTV... does not require tools... just an outlet....

Where is your work area? Is there power anywhere near it, or is it in an unwired garage? Thinking a small solar panel could be an option? So much depends on where, how far to a power source, and budget. Have seen solar garden lights use indoors at least for temporary source, but "best" solutions have to match your particular circumstances.

How much light to you need? Spot lights or just ambient lighting for effect?

I just love the little push on/off sticky mounted lights i picked up at a dollar store for my areas that needed some light. I got lucky and stocked up on 6 really cute ones. I just tap when/where I need the light and it's working great (going on two years now!).

https://www.hometalk.com/diy/decorate/rooms/stick-command-hooks-under-your-kitchen-cabinets-for-genius-lighting-29761267

https://www.hometalk.com/diy/kitchen-dining/under-cabinet-rope-lighting-25275012

https://www.hometalk.com/diy/decorate/rooms/easy-under-cabinet-lighting-and-hidden-cords-34493025

https://www.hometalk.com/diy/kitchen-dining/mini-kitchen-makeover-with-diy-under-cabinet-lighting-28484780?r=2