Your title and your question body are somewhat different. Until now, answers seem to have been directed at the title.
In fact, whipping cream with a gas siphon is a thing. Your idea is known, and widely used. You can buy whipping siphons with rechargeable cartridges for the home kitchen, and these sprays of "whipped cream" you get in the supermarket are exactly that, a one-time siphon which contains liquid sweetened cream and "whips" with the gas pressure when you press the nozzle. I believe there are also such siphons built in in some large all-in-one professional espresso machines, so the barista can float a little bit of whipped cream on your drink on the push of a button.
As the other answers mentioned, you need a siphon which is designed for it. Not only does it have to use NO instead of CO2, but it also has to be engineered to be suitable for dealing with cream instead of a watery liquid. Soda stream is not such a siphon. There are, however, siphons which are multipurpose (just not ones manufactured by soda stream). They can handle both the carbonation of lemonade and whipping of cream, as long as you use the correct gas cartridge.