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Marine Metal Products make the best aerators.
No reason to use anything other than an aquarium aerator at home. They're made to run non stop
What style "cooler" are you referring to? A typical minnow bucket doesn't really require an aerator during cold, winter months. I usually keep it in a cool place and change out a bit of the water now and then if I plan on keeping the minnows for a length of time. Like some lake water before heading home. Those "aerators" do nothing more than move the water around...they don't produce oxygen. Fresh and cold is the ticket.
There are a bunch of lithium rechargeable aerators on Amazon for $20. I picked one up that has a delay so it will run for 10 seconds then shut off for 10 seconds. Doubles the run time for when I'm on the ice. It can also run constantly when plugged in.Maybe you don't need an aerator for your minnows like some of those other guys, but when I spend $7 or $8 for a dozen shiners, I'm upset when they're dead a few hours later because I forgot my aerator at home. With the aerator they'll last all day and then some, same conditions.