Browsing on my phone just now, I don't see a clip of the sound to play.
If the sound you're talking about is the usual high-frequency static/hiss emitted to varying degrees by most amps, it makes sense that it would show up more in some cabs than others, as some are more and some less sensitive in that range.
If it is something else, as "whine" seems to imply, I'd investigate further - if there's an issue with the amp, you might cover it up by disconnecting the tweeter but you won't address the root cause.
I'm curious as to whether the level of the noise varies with gain and volume or whether it's fairly constant, even with those dialed down. Does it come through the DI as well? If you have another amp, it might be instructive to hook it up to the combo cab in place of the Combo Head.
As for disconnecting the internal tweeter, it can be done pretty easily - on my older, Italian-made CMD 121P combo, there isn't a "true" crossover - the woofer runs full range and the piezo is high-passed (and perhaps padded back).
There are some threads that discuss this as well as a mod some folks have performed, replacing the stock tweeter with a Monacor HT-30 horn - I had the mod done to mine, along with adding an on/off switch for the tweeter. Haven't yet played the amp that way at gig volume and am not yet ready to say it's a good idea, but I can confirm that, at home-practice volumes, output from the Monacor is lower than that of the stock tweet and that the impact of the tweet is more apparent off-axis than directly on.
Ditto for the stock tweeter - when I thought that there might be an issue with it (ended up being the amp, recently repaired) and tried running with it disconnected, the difference in high-frequency response between tweet/no tweet was more apparent off to the sides (where the woofer would start to beam higher frequencies more narrowly) than standing directly in front of the amp.
That said, the response with the tweeter disconnected might well be sufficient for you, depending on your tastes.
That said, I'd rule out other issues before modifying the amp.
(
@Doner Designs was one of the folks to try the Monacor mod - he details his experience here:
Markbass Tweeter Upgrade. How'd that end up working out long-term?)