Not sure if it’s 1.25 inches, but the softest dusting brush I have ever used was made by Panasonic for Kenmore. If you can find a New Old Stock Kenmore dusting brush, that would be your best bet. I even trust it to clean computer screens and laptop screens.
Not sure why, but all the current brushes made in China have very rough bristles, even if they are advertised as “horsehair” brushes. Classic North American horsehair dusting brushes are really, really soft.
My test for brush softness: run your fingers over the bristles. If they make any sound, they are too harsh. Soft horsehair bristles hardly make any sound at all.