Several thousand dollars? Purchase my plane tickets and I will come and remove it for you for less.
As long as you are not ham-fisted, removal of the CCU is not difficult. In the NSX Prime Library (link in top red banner) you will find a link to the 1991 service manual and page 22-84 in the service manual details removal of the CCU. The most difficult part in terms of the risk of damage is removal of the clock from the center vent and then removal of the center vent assembly from the center console. Note the location of the retainer clips for the clock and the vent shown circled on page 22-84. The rest is pretty straight forward. Just be careful to not drop any screws / fasteners down into the area below the center console during the removal or reassembly process because they will likely not be retrievable. Screwdrivers with a magnetic tip or a screw holder feature similar to this one can make life easier - there are numerous versions of this type, some better than others.
To minimize the risk of surface damage to the vent when removing the clock, apply heavy masking tape to the face of the vent where it borders the clock. You can back this up with a thin soft cloth around the removal tool as shown in the video; but, this can make it harder to get the tool into the gap. In the video he appears to use a metal flat blade screwdriver to release the clock retainer clips. I would not do that. This needs to be a really thin / long blade screwdriver. I would prefer to use an actual trim removal tool, something like the following.
Search for a bit and you can probably find them for less money. They are also available in plastic which reduces the risk of surface damage; but, the plastic ones tend to be thicker so they may not fit past the edges so easily. For prying the center vent out of the console you can apply heavy masking tape on the center console surface along the lower edge of the center vent to reduce the risk of scratching the console. I prefer to use soft plastic wedge trim removal or a good metal trim removal tool for this.
Do all of this when it is warm. The warmer the better because the plastic is more flexible and less likely to snap. This is not a project to do in the winter in an unheated garage.
Once the clock and center vent are out all the nail-biting parts are done. The rest is just tedious unscrewing stuff. As you sequentially remove stuff, put the pieces into zip loc bags along with their associated screws / fasteners or at least bag the fasteners individually and mark the bags. If you just remove the screws and dump them all into a cup, when the CCU comes back in a month or so you are going to be looking at the cup and going "so which screw goes where?".
If you own an NSX, you now own a classic exoti / supercar. You need to be prepared to pay for maintenance or learn to do as much of your own maintenance as possible.
