Controller schemes for mouse-based games

I wanted to see how other devs have gone about adding controller support for a game built for mouse-users.

My game is entirely controlled by clicking and dragging objects across the screen. My first thought was to use a virtual mouse like some games do, but that can’t be the best way to accomplish this. I mean, I hate when games do that, so I can’t imagine that players would be thrilled.

Any advice appreciated!