You can do it, but like mentioned above, you will need to consider the structural intergrity of the boat. Best bet is to remove the stringers aft of the last bulkhead and then replace them with new beefier ones that can withstand the load of the new engine placement, whather it be a bracket or notched transom. The transom should be reinforced for sure, and reglassed over on both sides to insure safety and strength. A good yard should be able to do this, but you might want to consult someone with an engineering background or a structural consultant to review what you might need as far as layup to be strong enough. Likely it will be a cored foam stringer and glassed with anywhere from 4-6 layers of glass, likely both bi and tri axial glass, there are many ways of doing it and every yard or consultant will give you a slight variation. There is not right or wrong way, they just might require more layers, cost different, or weight more or less. I think going to an outboard is a smart move if the boat is in decent shape and will not need major work, and that you plan to keep it for a while. The new added space can be used for tons of things...an indeck fish box, or an aux fuel tank, even a big livewell or dry storage boxes. You have tons of options for that space, plus more fishing room. You could add jump seats along the transom if you wish, or cooler and fish boxes, or leave it flush and just have more open space.
If I were doing it, I would add a bracket with floatation to handle a four stroke, and use the engine compartment space for 2 things....aux fuel tank, and a big fish well or livewell. You may also need to put the batteries down there on a shelf out of the bilge floor so remember you need access to them if they are to go there. You can get very creative with this project if this boat suits your needs well.