Should be a fairly standard control hack, though as it is an analogue stick involved here then it might not be quite as simple as some of the either on or off button hacks we do for other things.
Three main approaches, modified slightly by the game's own internal options.
1) You fiddle with the debounce section.
2) You find where the game itself reads the code for the operation you want.
3) If the game has some measure of control redefinition, even a selection of premade schemes, then it changes things a bit.
1) Switch bounce is a failure mode of switches, and also a feature. If you are connecting two plates of metal together (or two of any materials) there might be periods where the switch does and does not make contact from one millisecond to the next. To avoid problems with this changing between two reads during the same short period in a ROM many games/systems will copy the state of the controls to normal memory and operate from that for the next however long. If you can intercept this and fiddle with the bits in question then you can effectively swap buttons in a control hack.
For analogue this is harder, though could likely can still invert things (the analogue position tends to be a left-right range and an up-down range for most controllers rather than 4 numbers) or do some maths to invert the values.
In any case this is likely to be game wide so be aware of that.
2) Regardless of whether it reads a debounced section or the hardware registers the game will still have instructions that do something based upon what it sees. Find this and change what it looks for and you have your hack.
This will likely be specific to the individual action you are targetting. If there are many you want to handle then each will need their own hack. This does however mean you also limit the scope which is what you want here (for a wholesale A-B swap then nothing major doing it system wide but if it means you get to pull down to go forward, despite having a camera not having inverted controls then that would be less than ideal).
You have the added bonus here that the camera is a known concept within hardware (hopefully it is not a move the world rather than the camera game) so you don't have to figure out some more esoteric result and work backwards (if I want to change a bullet firing button I might have to look at ammo as it will be depleted by that and work backwards from there).
3) If a game has control options then presumably you would have done that, though some might opt to allow the truly odd combos if there are a few restrictions (if you want the start button to be run then you do you and all that). A prebaked selection still means there is some kind of abstract fiddling going on somewhere underneath it all so you get to figure out how to change it, though you can still go for 1) or 2) with these if you don't want to figure out the game's mapping format or find the approach better for your given hack.
4) Some people rewire the controller. 10 minutes soldering and it working on every game instantly without hacks which would otherwise have to be done for each game (or multiple actions within) can be what people want. Probably not what you want in this case, though if looking is related to Z targeting you could do an invert if this button is pressed option easily enough with one of the programmable chips (which would also open the door to easy rapid fire, macros and more besides).