That would be the wood used to surround the tang of the blade. The blade tang would slide into the wooden tsuka and then be pinned in order to keep it from sliding out. The tsuka would generally be covered with rayskin then have a Japanese style wrap over that to complete the handle. Some of the tsuka cores from some manufacturers have been known to crack easily or be cracked from the factory.
Cold Steel has been accused of having this problem a few years ago and I don't know if it has been corrected.
The reason that is important, as a side note, that if your handle comes apart in a swing, you can have a couple of results. The sharp sword flying through the air like a spinning pinwheel of death is one negative consequence.
You can also end up with a hand full of sharpish, vibrating steel if your handle disintegrates. (often the tangs are not what you would call "hand friendly"
Lots of things can go wrong when cutting anything with any kind of edged weapon.
Add in to that more momentum and tons more edge when you start using swords, and swinging them about. Then multiply that by having a handle construction that is absolutely not ideal for continued rough abuse. ( I know people will yell and scream that the handle design of the Japanese swords is really all held together with a bamboo pin, and a single bamboo pin at that.)
I have no doubt that a master sword smith, fitting a quality wood handle has enough skill to make a sword in this fashion that will last for generations.
Take that same traditional bamboo pin retention construction and have it made in a factory in the cheapest bidding factory in a third world county, and you may have problems.
Also, you have to be savvy enough to take the sword apart and make sure the pin is still in good shape after use.
That is why it is a great ask advice before spending the cash.
I have a European sword that I have no doubt will withstand years and years of stupid cutting abuse. It is also a bit heavier than a sword of that style should be for "combat".
It was designed as a "beater" It has a very heavy sturdy tang with a wood core handle under a leather wrap which is also held in place with cross leather straps and pins. A heavy ricasso and very stout guard and blade.
I would not hesitate to use it for cutting from a concern over the sturdiness of the construction. Now, it is a 5 lb piece of sharp double edged steel, so that alone would give me pause on using it for cutting. I am a big strong dude, but like I said, there is a whole list of things that can go wrong when cutting. Bad form can cost you the use of any of your appendages if you have a bad day.
Everything I have heard about the Cold steel line of swords indicates that they tend to be heavy for style (including the Grosse Messer). They should be sturdy enough for abuse. But be aware that a failure can mean disaster.
Watch your backdrop, footing, wear more protective clothing. Steel toed boots would not be out of line (I know that people who train in traditional cutting would laugh......but we are talking about people swinging sharp swords with no training).
Just use common sense.
In the price range of those CS swords, and if what you are looking for is out and out abusive use, I would recommend looking at the AK47 (Busse), the Swamprat Waki (Swamprat), and the Scrapyard Waki. Those family knives are not traditional designs of course, but they run from about 900 down to 200 and all have forever warranties.
The way they are built and heat treated, I have seen them bent 90 degrees without taking a set, and 180 with out breaking.
They are lighter, and easier to control as well.
If you are looking for a traditional design and appearance, others will have better advice than me.