My guess is no, you are essentially just streaming video to another device and that is all software can do. The raw video rendered by your gfx-card is a pretty huge chunk of data (at 1080p and 60fps this could well be 700mb+ per second!!!). It takes processing power and time to compress it before it is send over. When you are watching a live stream on twitch you have a smooth experience because you are only seeing one end of the connection and don't interact with the video, as soon as you type something in the chatbox and have to wait for the streamers response you realize there is a delay of often a couple of minutes. For streaming a video on twitch that is fine, since the interactive part is not a priority, the smooth video is. but you don't want to wait a minute until you finally see your cursor move after touching the mouse, so the software has to handle this problem differently. Of course i don't know how it does that, but it probably has to drop frames which would make for a choppy experience.
Something that might make everything a bit more bearable is reducing the resolution of the extended desktop(the laptop screen) as much as you can bare.