jb, though I can't answer your question about the Uggie thread size I just want to offer one caution. When you change the bead size to a smaller one it may well cause your gun to shoot higher, i.e. the pattern may print higher than it does with the larger bead.
I bought a vintage 20 ga. pump last year with plain barrel and small bead. It patterned high for me, so much that I knew it would cause fringe hits and misses. I removed the bead, measured the thread size and ordered a larger bead in the same thread pitch and shank size, at the suggestion of a friend on here. It brought the pattern down perfectly.
I know we don't use the bead as a sight, like a rifle, and many believe they can shoot just as well without a bead. I won't argue with them, but for some reason I see the bead in my peripheral vision, as I focus on the bird, enough for it to affect where the pattern prints.
Not trying to suggest you don't get a smaller bead, just offering something to watch out for.
Best, SRH