There is a workaround to this, confirmed (by me) to work for Dark Souls III, Dragon's Dogma and GTA V. This has only been tested wired because I don't have a BT chip in my rig, but it should work wireless by choosing the correct device.
First you need to quit anything that could grab the device before DS4Windows, like Steam. On my rig it's only Steam, but I've heard that some other things may have to be closed as well.
Then, before starting DS4Windows, open the Device Manager. Note that if you have your DualShock connected, there will be one entry under "Human Interface Devices" called "HID-compliant game controller".
Once you start DS4Windows, this entry will be duplicated, you will now have two "HID-compliant game controller"-devices. Disable one of them by right-clicking and choosing from the menu. On my rig it's always the top one that should be disabled, but I don't know how Device Manager orders its devices so it might be the bottom one for you.
If you disable the incorrect entry, the controller will disappear from DS4Windows, so just re-enable it and disable the other one.