swagger and sashay suggest an element of strutting, arrogantly in the former case, with a certain contrived, "look-at-me" nonchalance in the latter.
My own hunch, based on nothing, is that the Earps were not swaggering, sashaying or strutting at all that day. (They may have done so on other days, which is where the confusion probably arises.) Or, if they were, then, at most, only intermittently, and even then, more furtively than not. (I cannot explain how one swaggers, sashays or struts furtively. It would seem oxymoronic, and yet, so too the deafening silence through which they strode. On shank's mare no less.)
No, I firmly believe that they were....mincing. I believe that all the evidence indicates, or SHOULD indicate, eventually will indicate, as it must, or is rumored it must, that they were mincing.
Except Doc. Who, apparently, at least from all appearances, those of which were presently are aware, or can imagine becoming aware, was limping.
I have forgotten the original question, but hope this helps answer it, whatever it was or may once have been.