It is great that you are thinking about correcting your bite. With skeletal issues such as a slanted jaw, surgery is indeed required in order to achieve a good stable bite.
However depending on the degree of skeletal discrepancy (slanted jaw) braces / invisalign are still options for you to consider in order to straighten out your teeth and give you a good smile. Straight and aligned teeth can be achieved but there are limitations so it depends on what your ideal smile is!
My suggestion would be to consider all your options and if needed seek a second opinion. Hope this helps and all the best