As long as the skimmer fits, it'll be fine. You can build or buy a stand (even adjustable) to set the skimmer depth, so setting the baffle for that chamber higher than the required 9" for your skimmer isn't an issue.
The return chamber is the more vital part, as that's where the water level will vary the most. You want to be sure that you have enough extra volume so that when the pump is off (whether you shut it off, or if/when the power goes out) to account for the water that will drain down from the tank until it's below the overflow in the DT (display tank,) as well as returns, as they will start a siphon and reverse flow into the sump in such an event as well. You want to be sure when your return pump is off, your DT can drain to this point without overflowing your sump.
Keep in mind that if this results in the water level in that chamber rising higher than the baffle that water flows over the top of between where you have the skimmer and return, it'll raise the level in the skimmer chamber as well. That means it'll change the water level your skimmer is in. Not a huge problem, just something to be aware of - ie if you shut off your return pump for maintenance, you may need to shut the skimmer off as well.
The return chamber will be the section that varies depending on how much water is in the system, so it'll be where you'll have an ATO if you're using one for evaporation. Otherwise, when the system is running, it's generally best to keep the water as low as possible without the return pump sucking air, so you have more empty volume to accommodate that extra water from the DT when the return pump is off.
