I'm pretty sure changing the sound files that trigger with the emote command would require file editing. AFAIK there isn't any sort of emote that you can load a sound globally from a source outside the PIGGs. If I'm wrong someone will correct me but I don't think there is an easy way through emotes.
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I would assume if you went rifling through .pigg's you might be able to change what certain sound emotes sound like for you, but not for anyone else nearby, they'd hear what the standard is.
I know this works with music and certain sound effects (the vahz flies and vomit always come up in these threads as being the first to be rejected), but the sounds that a particular emote plays, i'm not sure.
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There's a program called CoH Splasher that does just this. You can find it here .
Start by reading the beginning of this thread carefully. In spite of the thread title, sounds can be replaced as well as silenced.
Boombox related info is here.
[Edit] The previously suggested program apparently won't work properly on anything but Windows XP.
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Many thanks to all. 
I wasn't sure how my post was going to be received (I'm quite new to these parts), but I'm glad there seems to be a supported method. I'm disappointed that any adjustments are local client only. I'd like to share some music, but, c'est le vie.
@BayBlast, I have windows xp 64bit pro edition, which has occationally had the compatability issue or two. Think that I might be ok?
Sure, give it a try. If there are any big quirks you always have a fall back plan.
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I can easy assume the answer to this question, but on the off chance I'm wrong, I'd like to know for sure.
Is there a way to instill other sounds and music clips onto the Boombox emotes than is already available? I've taken a liking to the Pocket D dance floor rif, as short as it is, and would dig it if I could play it on my boombox. There's a few other tracks I've heard here and there in missions and out and about that are far better than some of the boombox tracks.
I've heard of how some things are adjustable in game, and that some emotes are gifted from getting badges. So I thought I'd ask, just in case there is a way.