I was wondering if it is possible to play the Switch on the laptop so it can be played on the screen. Can anyone help me
How do you mean dat exactly?
the external monitor connection on laptops is not an "INPUT". Only output can be made there, no input of image signals.
Yes will work.
Since a laptop usually does not have a video input, you would have to retrofit one, e.g. With a capture card.
You then connect the Nintendo Switch to the capture card via an HDMI cable and the capture card to the laptop via USB.
Then you play back the video signal with a suitable program on the laptop.
However, a decent capture card usually costs more than a simple monitor.