I did some digging and Switch simply does not support HTML5 games. Over the Scirra forums, the dev of Construct told they did contact Nintendo about it to port Construct to Switch but they were ignored pretty much. So, if you really want to target Switch, your only realistic option is to port the game over to a native engine, maybe hire a company to do it for you.
There are studios out there who port games over to other platforms, for example Sick Head Games. Basically you give them everything, all the design docs, assets, and they build the game from scratch (using MonoGame I believe) for any platform you choose including Nintendo Switch. But certainly it won’t be cheap but it is an option to consider if you have success on Desktop and Mobile and you don’t feel like you can do it your self.