Video camera with fractional shutter speed

Hello,

I have Panasonic HC-770V camcorder and want an upgrade to a 4k 60fps capable camera.

however, i want to be able to set the shutter speed manually into fractions like 60.2 fps or so. My content that I want is to shoot CRT videos of retro game consoles which are not perfect 60 fps, thus will introduce a black line moving once in a while. Plus, I will use it for other youtube videos which won't be a problem for any camera.

My budget is about 400$ since I don't want anything fancy, just these little features. My currently liked camera is DJI action 5 pro but I didn't see the shutter speed details so I assumed it does not offer it.

please give me your recommendations.

thanks