Without a middleman server, this would require you to embed your secret key within the app, allowing your customers to access said secret key, which would allow them to manage your Stripe account. Not a good idea.

If you're not embedding your secret key within the app (i.e. you're only generating a card token using the public key), I don't see a problem with embedding a checkout form directly within your app, though that's rare to see.

Since not many desktop app do this, it will surely raise concerns. How about direct to website for completing the payment ?

Thanks for confirming "surely raise concerns". That is enough for me to think of an alternate solution.

Can you not use a usb card swiper? I dont see the problem here.. What is the use case? What is an average user? Do a survey about these questions to your potential users?