I think it should work.
I checked the wiring diagram for my D200E AKG, and like your Shure, it has pin 2 and 3 as hot and return, with pin 1 to ground, so the same adapters that work for me should work for you.... However, the AKG diagram does not illustrate pin 3 and case connected, so that may remain an issue.
It looks like the Shure is set up to ground the XLR case and pin 3 together. I don't know if that is appropriate for your situation. You could try looking inside your current cable at the end that goes into the mike, and see if it the XLR is set up that way in the cable as well. If you decide to try another cable you could experiment on your current one, and try desoldering the connection between the XLR case tab (the little bar in the diagram) and pin 3. A bunch of old Neumann mikes were also set up that way on purpose, since it helps prevent environmental noise pickup on such mikes (but not all mikes).
If you do ground case and pin 3, i think it has to be that way at both ends, and I don't think the Sony is set up that way. You can do the experiment and find out, if you are able to put your current cable back the way it used to be.
Here's another issue that might be relevant. On my Sharp minidisc recorders, it is possible to engage a true MONO recording function, which i used to do when using one mike going in via TRS. This can not be done on the Sony M10. I don't know if your current adapter cable made use of the minidisc electronic summing to mono, and is failing to ground one side of the M10....I have my suspicions.
good luck