Post a pic so we can see the wall. Exterior siding type can make a difference in how you finish it off. For me, that would be stucco, and if your careful, no wall repairs necessary.
You can do this without cutting the inside drywall. It just takes a little imagination.
First remove the existing box:
Using your replacement box, make the size of the new hole and cut out the siding/underlayment/whatever to expose the wall innards. I'd use a vibrating multi-tool. Mine is HF, and works fine. If possible, verify wire location so you don't damage it.
If the box is plastic, use a sawzall against the stud and cut the top and bottom nail. Slip the blade between the box and stud at the center and slide up or down until you find the nail. Use a fine tooth metal cutting blade, not a wood blade. Be very careful not to over cut and nick the wire, which should be nailed to the stud nearby. I presume a metal box is similar, but its been a while since I've come across one.
Replacement: Use a NEW work box. Cut off the nailing ears. (You already have a sawzall and a multi-tool, right?)
Drill two mounting holes on the stud side and predrill for drywall screws. Put box in hole and screw into stud. The holes should be far enough in the box to hit the stud, but not so far as to make a bad angle for screwing. If you can get a ratchet and bit in there to get the screw in straighter, that is preferred, but screwing in at a bit of an angle is fine. With a double box, the angle isn't bad. Single boxes are a tad more problematic.
If the box is too floppy on the unsupported side, you can add a battleship, but I"ve only needed to do that once or twice. (point in fact, you could use a eared metal box and battleships and not touch the stud too)
Place electrical tape over the screw heads. Install your stuff. Its probably advisable to pull the wires into the box in advance too.
I've done this many times. It works well.
My bigger concern is how are you going to run the wiring? I'll leave that alone for now as well as how you fix the siding, whatever that is.