Yeah dawless is kind of a misnomer, named after the thing people dislike: sitting at a computer.
As far as I can see, most dawless performances are still recorded into a daw. Some might even mix it in one.
Of course you should do what suits you. If you’re having fun, it’s good music. So if you set the mix before you perform and just record into a field recorder, all the power to you.
If your mixer has busses or multiple master outs you could even hook up your phone and record directly onto there. Easy sharing 👍