Is a NRTL / UL mark required for battery powered products?
NRTL marking is not required by law, but is a requirement of your end customer and/or insurance company, including the distribution chain. For example, if you want to sell a toaster through Walmart, you don't (legally) need a NRTL mark, but Walmart may require it.

You didn't mention where the product is going to be used. Some applications do require NRTL marking for battery powered devices like this, but they're rare. I'm working on a tiny battery powered device that operates in a Gas Station, and we are getting the product UL certified as requested by the customer.

Remember that when it comes to NRTL, it's not just the upfront cost, but you also have to pay for annual factory inspections. It can be more expensive than you originally think. And also, they test everything, including the label you're using (we had to switch labels) and plastic enclosure, etc.

If the batteries are user-replaceable, be sure that you have some type of reverse polarity protection so that if the user puts them in backwards it will not break anything.