I would not suggest doing that as it might ruin the headphones or at least decrease the value of them. Using adapters is more sophisticated way for old equipment.
Those both connectors looks like mono connectors, if one of them really is for mic then you will not have stereo sound out of them. Do you happen to know model of the headphones? Or could you take a picture of them? Would make it easier to point out correct adapters.
You make a good point that I didn't really see on the pic. Both connections are T/S, which most likely means a signal and a common on each connection.
So, that is either a mic and a single speaker, or 2 speakers. Nothing else makes sense.
I agree that an adapter is the easy way to handle this (I linked one), and it allows to return to original config when needed.
But, looking at that connector and the sony name, I really doubt these carry much value. I would personally have no reservations about clipping a terminal to replace with one that suits my needs. I guess the only reservation is that these wires may be tiny and tedious to work on, but I have the tools to deal with it. Any good electronics tech can make a swap like that and have very professional final results. In fact, I have repaired gaming headsets and ended up with results that looked better and were more robust than the originals.
