Ehm, sorry but I cannot explain how to make a good whistle in like a couple of sentences. I've been doing that for 5 years and it took me a half year and more than 20 prototypes to perfect the square whistle. So you would have to learn the necessary skills and make yourself familiar with some tools like a "flutomat" software to calculate hole-size and other measurements. It would be all but useless if I gave you some calculations if I don't even know what type of material (wall thickness, diameter, etc) you'd be working with. Every millimeter difference would make new calculations necessary. So I guess your best bet is to buy a Susato with a thumb rest. It's not like I have some "secrets" I don't wanna share but it takes time and effort to come up with a good, in-tune whistle. There is more than enough material online on how to make whistles. And there is no geometry needed to come from 12x12 mm to a round diameter. The formula for the area of a circle is r^2 times "pi". And 2 times r is the diameter you need for any flutomat software. So I use tubing with 14 x 14. Inner diameter 12 x 12 (not 13 as stated above, my bad -- wall thickness is 1 mm)
12 x 12 = 144
144/pi = 45.8366236
square root of 45.8366236 is 6.770275 -- take it times 2 and you get the inner diameter of a round tube which you can then put into a flutomat software to calculate the hole sizes and spread of the holes. 13.54055 mm is the number you'll get. This is the formula you need when using a flutomat software with a square tube. Basically just translating the square profile into a round one.

Sorry, I didn't mean that I'd ask you to calculate it for me. I meant that if I could get square tube identical to yours, would you be willing to share the hole locations and sizes that you used?

I am a new whistle player who has a thumb injury that makes holding a narrow-body whistle very difficult. I'm currently playing a tweaked OG Clarke that I've glued a big leather pad on the back of to be able to hold it.

I will admit to a prejudice against plastic instruments, as I always fear they will sound like the elementary school recorder of my youth.

Wood whistles are not everyone's cuppa.

This thread came up again and I wonder what you came up with. Nothing to be ashamed about if you make a frankenstein whistle by the way. It is the music that counts, not how they look.