Hi, I had a similar problem a long time ago with another game.
I found a nice (and now cheap 3€) program on Steam called Controller Companion that lets you move the courser, right and left click. (XBox Controller only i think)
And with that, you be able to cover the most basic interactions in TiTs
You can also bind buttons directly, so if you invest a few minutes and think about which buttons you really need, you can provide a good portion with a shortcut. (Backbutton for second bindings)
I don't know if there are other programs that do the same, it's been a realy long time since I've looked for a solution and my Controller eats dust atm.