P. Johnson does some of those "zero structure" designs. I think it works on some people (like Patrick himself), but it's not the most flattering thing on other guys. You have to have the right physique and character for it.
If you do it, ask your tailor if he's going to cut a side body. Years ago, I thought about commissioning a shirt jacket with a separate side body because it seemed like you could get a bit more shape out of the waist. That'll mean that you'll have to go to a "traditional" tailor and not just a shirtmaker, which will drive up the cost. And you'll be paying for a whole lot of stuff that you're not getting, like that canvassing and structure inside. Might be worth trying on RTW brands that are similar (e.g. Barena) to see if you even like that zero structure look (I think Barena has no structure, but if not, it's pretty close).
Anyway, I would probably go with a spring/ summer fabric. Maybe linen or something.
I don't know about Bel y Cia's, but Justo Gimeno's Tebas have a bit of fusible in the chest and some shoulder padding. IMO, that's what makes them look a lot better than totally unstructured shirt jackets.