David, I’d check with your fellows over at trek-lite.com. I think you’ll find lots of info about poles suitable to support small pyramids in a gale.
Light trekking poles like Locus Gear’s CP3 poles are made with 16mm, 14mm and 12mm pole sections. In my experience, a pole 12mm in diameter is too bendy to support a small mono-pole pyramid with complete confidence. This is assuming 12mm diameter with 1mm wall thickness, so this type of pole stock would be advertised as 12×10 mm (12mm outer diameter, 10mm inner diameter).
However, MLD sell a pole for supporting their small pyramids that is 10.75 mm OD. They do not specify the inner diameter, and I suspect their pole stock is a little thicker than 1mm. (MLD uses unidirectional carbon tubing, which is a bit unusual in the industry; the only unidirectional pole stock I’ve been able to find for sale on line in small diameter like this does have wall thickness greater than 1mm).
Another example of an available pole meant to support small pyramids is Ruta Locura; they recommend 15mm pole for pyramids this size. I think they are probably using 1mm wall thickness, but I’m not sure.
I have a 14mm (14mmx12mm) pole for a 135cm-tall pyramid and think this is adequate. 16x14mm would be stronger still and weigh about 1 ounce more for a pole around 140cm long. However, I have read about guys in the UK who sometimes pitch their 135cm-tall Luxe Hexpeaks with two trekking poles side by side.
The Colorado-based company, Seek Outside, is known for prioritizing strength over weight. The pole they sell to support their 145 cm-tall Silvertip hexagonal tipi has an OD of 23mm! I think that might be overkill, or in any case recommend the largest diameter you might ever need to consider.
Here is a post that explains the relationship between diameter, pole rigidity and pole strength: https://backpackinglight.com/forums/topic/myog-cf-tent-poles/#post-3730154