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Buy one of the mutes from Tennessee Tech. They don't cost much money and they aren't stuffy at all. Humes and Berg (Stonelined) makes good tuba mutes of all kinds, for all kinds of tubas (even recording basses and sousaphones!) If you need a plunger mute, I suggest using a plastic garbage can lid (I learned this from watching Howard Johnson and it works so well!)

Here is one of many threads on the subject.
viewtopic.php?t=6643&highlight=mute
Back when I actually needed a mute, I had the H&B aluminum mutes, both sizes. They gave a different tone color and didn't totally destroy the intonation. My school had a stonelined and I thought it was junk - just made the horn sound muffled and stuffy.
Here is another interesting thread pertaining to mutes (and whether you need them )
viewtopic.php?t=4848&highlight=mute

2 words:

road cone

for added pleasure, throw a towel or two down into the cone for extra stuffiness and weight

blaze orange looks great against an orchestra of all black and white... the back row will finally get what they paid for

For sousaphones, there is one word: Volleyball.

Hank74

Have you ever tried a road cone as a mute? They are very heavy. I really did try it once, covering up the big opening with duct tape and a pizza box. It's not good, though the sound is quite nice. You just feel like you are trying to hold the Governor of my fair state inside your tuba.

Ahh... this reminds me of that one time my friend at his high school help roll a sousaphone a quarter mile down a hill...

Did it look like the proverbial cigarbox car from the wrecking yard afterwards?

Well... it looked like that BEFORE they rolled it down the hill. The rest was just icing on the cake.

Mute? Just finger everything with an alternate fingering using 4th valve and drape a towel over the bell to the appropriate closure, like a bass drum player does.

Seriously, I'm a great H&B fan.

Well, I'll get flamed for this, but what I found most effective in the symphony was the use the plunger end from a metal trombone straight/Harmon combination mute (when I had one hand free). Espescially when a straight mute was called for.

Being able to direct the sound and choose the amount of muting were big pluses. And I could make sure that I didn't mess up the intonation. It was light, and when the conductor looked back, they saw me using a mute, so they were happy. Because the sound was adjustable so that you could project, yet have a pronounced effect, I don't recall a single composer who ever commented.

I had to do it one night because I was desperate. I had trombone mutes around to use with my flugelhorn. I was very surprised with the result, and never looked back.