I don't think we can have the choice for constant velocity motion. Unless we imagine something for which there's no evidence.

The way I see acceleration is your velocity changes from what it was before. So everybody knows it's changed. Not everybody may agree on how fast it was before, but at least they agree how much it changed by.

So it doesn't require any special reference frame. If you like, one usable frame would be the intertial frame of the previous state of the object before its speed changed.