I've been practicing to better understand and apply commuters and conjugates in big cubes. I've solved the majority of my 7x7 cube but got to a point where I have two side pieces flipped (so blue-orange is on the blue-yellow spot and viceversa). I've tried making cycles which scramble more of the pieces, but when I resolve it I get to the same point again. Can it be solved just with these tools or do I just need to learn a specific algorithm?
It is not completely clear what your cube looks like, but I am going to assume there are two wing edge pieces that need to be swapped.
A single swap of two edges is an odd permutation while any commutator and conjugation of a commutator is an even permutation. It is therefore impossible to solve with (conjugated) commutators only.
One way to solve it is to perform a single slice move - a quarter turn of a slice containing one of the swapped edges. This is a 4-cycle of such edges (an odd permutation as required) after which you can solve those edges using commutators only. Of course that slice move also disturbs centre pieces, but those can also be fixed using commutators.
One easy way to fix the centres is this:
Hold the cube so that one of the swapped edges is along the UF edge. Let's call the inner slice containing that edge the
r slice. Do the move sequence
r U2 r U2 r U2 r U2 r. This returns the centres but still does an odd permutation on the edge pieces. You now still have to fix the edges with commutators, but as they are now in an even permutation, that is possible.
Note: I have described this as if there is only a single pair of swapped edges. On a 7x7x7 cube there are two types of wing edges, inner and outer ones. These two types can each have this parity problem independently of each other. Both can be solved the same way.