The only potential problem with changing substrate can be the amount of good bacteria that can be lost. Bacteria lives all over tank and every tank is different. Many people assume most of their bacteria in in their filter(s) but this may not be the case. Due to a variety of factors a tank can have a decent portion of the bacteria elsewhere in a tank beside the filter. there is no way we can know where the bacteria in out tanks is.
Planted tanks have a much more biologically active substrate than those with no plants. In planted tanks there are active types of microorganisms all the way down. In an unplanted tank there are no nitrifying bacteria after about .5 inch depth (1.3 cm) as there is not enough O when you go deeper. Plants will transport O to the substrate specifically to foster bacterial colonies deeper in the substrate.
The upshot of this is that one can never know for sure how much bacteria may be in one's substrate but it does insure that one is aware that it can be a consideration when changing substrate. So how can you use this knowledge to your advantage?
For one, it should alert you to the need to monitor ammonia and nitrite levels after one changes substrate.Small spike will disappear pretty fast a the bacyteria catches up. However, larger ones need to be dealt with before an harm might result. Some folks will replace substrate in stages. They will replace 1/3 or 1/2 at a time which will minimize any potential problems. Another strategy is to park the fish, as you are doing, make the changes to the newly setup tank and then do a mini-fishless cycle on it. You add 2 ppm of ammonia to the new tank and then monitor it. Because you are not removing anywhere near all of the bacteria by doing the change, the remaining bacteria can easily double in a day to makeup any loss as long as there is some ammonia in the water for them.
The point of the ammonia addition is that you quickly can tell how cycled the new setup is. You may be surprised how fast the new tank becomes safe. A day or two usually does the trick. Your fish should be fine parked for a day or two. They wont even have time to get used to the temporary tank and begin "arguing" before they go back into the original tank. You should also monitor ammonia in the tank where you park the fish. Because it is a short term stay, you can simply change water if this is an issue.
It is also quite possible that, after you replace the substrate, the tank will be ready almost immediately. There is no way to be sure of this unless you do the ammonia addition as mentioned above. Look at what you are doing as if you were setting up an new tank but having a lot of bacteria seeded at the start. Such cycles go really really fast when there is a decent amount of bacteria at the outset and you will certainly have that from the filters and other decor in the tank which is also hosting some bacteria.
One last note here. The process of changing substrate can be messy as things perfectly happy in the substrate get disturbed and get into the water. This itself can cause ammonia to spike some. It may also get into your filter during the change or soon after as you work to clear stuff from the water. This "debris" can create ammonia as it breaks down and even if this is not a problem, the filter can become clogged from it. Be sure to rinse the media gently after the change to clean it of excess gunk.
Overall, you should be fine if you monitor ammonia in the tank for the next couple of days after you do the change. You may also find that everything is just fine and no action is needed.