I just sold a 2003 KX 250 with a 2001 KDX 220 engine. The 250 frame allows you more room, but it complicates the exhaust as compared to the 125. I would recommend selling the 250 and finding a 125 if you can. The other thing to consider is that year KDX engine has an issue with breaking KIPS valves, and they aren't made any more and are very hard to find in one piece. It might make more sense to flip that one and look for a 1997 and up engine.
If you want to keep going, you will need to trim the swingarm and bearing races. Also, you will need to do something with the pipe. That year KDX is not a perimeter framed bike, which means you can’t use the KDX pipe in the KX frame. You may be able to use a later model pipe, but I’m not sure the flange is the same. The motor mounts will not line up, so you will need to modify them.
The end result is a really nice woods bike. I just think it might be easier to start with different models.