Currently there are only 2 types of hard booze on the menu: smoked Bourbon and Godiva chocolate liqueur. Since this is a QS wouldn't be surprised if the alcohol is premixed with other ingredients of the listed shakes so I suspect that unfortunately customization is hard /impossible to do.
Current menu:
https://www.disneysprings.com/dining/d-luxe-burger/menus/Lunch And Dinner/
They might be able to add some of the dry ingredients of the s'more shake to one of the alcoholic ones though. Not quite the same but perhaps a facsimile that'll still make you happy.