I'm lost with this terminology, having never played a horn. I also fixed on your use of "tremolo" vs my use of "vibrato" and had to look both words up.
tremolo is variation of amplitude/volume
vibrato is variation of pitch
I'm hearing pronounced vibrato in Muggsy's playing on this record, which I always thought made him sound like the exuberant teenager he was when he made this record, and I find it compelling and completely mesmerizing nearly 100 years after it was recorded. I agree that he didn't keep the vibrato throughout his career, and you seem to indicate it may have been a youthful way of playing he grew out of.
I also hear pronounced shaking on most of Bix's Wolverines sides, I just heard it on Royal Garden,
Susie, Copenhagen, not so much on Big Boy. I'm not so sure it's vibrato, i.e., pitch variation. I don't even know if it's possible to play a horn tremolo. Could it be an artifact of recording, or replay via computer, since most of the instruments seem to do it? Although I noticed it pre-computer.
This shaking is part of what gives these early sides their charm for me, since most players and most instruments seem to do it. Certainly Louis was the best and most dramatic at it, but on the Stomp 6 sides Muggsy gives him some major competition, in my opinion.