How to remove the pop-ups on shadowplay/ Nvidia share

Based on what you've described, I think this post has a solution.

Using a wired/wireless controller connected to the GFE PC instead of the streaming device

Normally, Moonlight sends controller input from the streaming client which gets sent to the game by GFE. If you want to connect a controller to your PC instead of the streaming device, GFE can cause some problems because the emulated controller still appears to games as controller 1. Luckily there is a workaround for this. You'll need to rename the DLL that Nvidia is using to send controller input so it won't be used anymore. On 32-bit and 64-bit Windows, rename rxinput.dll to rxinput.dll.old on in C:\Program Files\NVIDIA Corporation\NvStreamSrv. On 64-bit versions, there's another copy of the DLL in C:\Program Files (x86)\NVIDIA Corporation\NvStreamSrv which you'll want to rename. You may have to do the renaming again if GFE does an update, but it should allow you to use your controller normally on games that only support 1 controller.

(I bolded the instructional portion of the quote for ease of access)

It will also be necessary to rename rxgamepadinput.dll and rxnvgamepad.dll, both located in the aforementioned directories.

This will have to be done afterwards in whatever editing program you use as Shadowplay just records (and now uploads to selected services) the gameplay.