If you go into Dock Settings, I believe you can select placing the Dock on the left side of the screen. This would place the Trash in the lower left corner. It would also make all the Dock items sit on the left side.
Alternatively, you can move items to the Trash by right clicking (control-click) and selecting move to Trash (or eject for an external drive). That is actually faster than dragging things.
I guess this is ultimately about personal preferences. I don't see what left or right handedness has to do with this. There are multiple items on the left side of the screen (Finder icon in the Dock; Favorites; Locations; Sidebar; various Menu items) and those of us who are right handed don't have issues with that. I guess it is the dragging that you find inconvenient, which I can certainly understand, but Control-click (right click) might minimize the dragging that you need to do, or even eliminate it.